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Bridget Sena Borbor, Lewis Brew, Joseph Acquah
Earthline Journal of Mathematical Sciences, Volume 11, pp 211-228; https://doi.org/10.34198/ejms.11223.211228

Abstract:
Unemployment is one of the major socioeconomic issues across the globe in which Ghana is no exception. The unavailability of jobs and its creation as being searched by persons belonging to the labour force actively looking for jobs makes the problem escalate rapidly in a growing economy. In this seven state model, we analysed into the three main economic sectors of Ghana to investigate how unemployment, employment, and newly created vacancy creation behave at equilibrium on the three economic sector levels. Moreover, we analysed how in a specific sector, the dynamics of the state variables control unemployment. Further analyses on the parameters indicated that, an increase in the rate of newly created vacancies results in a decrease in the number of unemployed persons and an increase in the number of employed. We assumed that a jobless person who is available for work but fails to make an effort to seek work is not part of the unemployed class among others. It was established that the model has one nonnegative equilibrium point. Lastly, we analyse the impact of perturbation of some parameters on the number of the unemployed and employed persons at equilibrium.unemployment
Brice Réné Amougou Mbarga
Earthline Journal of Mathematical Sciences, Volume 10, pp 195-209; https://doi.org/10.34198/ejms.10122.195209

Abstract:
The aim of this paper is to use a correspondent theorem to characterize containment of a degenerate $2$-factor injective subdirect products. Namely, let $\Omega,\Lambda$ be degenerate 2-factor injective subdirect products of $ M_{1}\times M_{2}\times M_{3}$, we provide necessary and sufficient conditions for $\Omega\leq \Lambda.$ Based on a decomposition of the inclusion order on the subgroup lattice of a subdirect product as a relation product of three smaller partial orders, we induce a matrix product of three incidence matrices.
Ahsan Fayez Shoushan
Earthline Journal of Mathematical Sciences, Volume 9, pp 93-103; https://doi.org/10.34198/ejms.9122.93103

Abstract:
The goal of this project is to offer a new technique for solving integro-differential equations (IDEs) with mixed circumstances, which is based on the Hermite polynomial and the Least-Squares Technique (LST). Three examples will be given to demonstrate how the suggested technique works. The numerical results were utilized to demonstrate the correctness and efficiency of the existing method, and all calculations were carried out with the help of the MATLAB R2018b program.
Abbas Kareem Wanas, Hussein Kadhim Raadhi
Earthline Journal of Mathematical Sciences, Volume 11, pp 199-210; https://doi.org/10.34198/ejms.11223.199210

Abstract:
In this paper, we obtain upper bounds for the first two Taylor-Maclaurin and for two new families Υ_(Σ_m ) (η,γ;α) and Υ_(Σ_m)^* (η,γ;β) of holomorphic and m-fold symmetric bi-univalent functions defined in the open unit disk U. Further, we point out several certain special cases for our results.
Earthline Journal of Mathematical Sciences, Volume 11, pp 183-198; https://doi.org/10.34198/ejms.11223.183198

Abstract:
The object of this article is to explore two subclasses of regular and bi-univalent functions subordinate to Horadam polynomials in the disk $\{\varsigma\in\mathbb{C}:|\varsigma| <1\}$. We originate upper bounds for the initial Taylor-Maclaurin coefficient estimates of functions in these subclasses. Fekete-Szeg\"o functional problem is also established. Furthermore, we present some new observations and investigate relevant connections to existing results.
J. B. Omosowon, A. Y. Akinyele, O. Y. Saka-Balogun
Earthline Journal of Mathematical Sciences, Volume 11, pp 173-182; https://doi.org/10.34198/ejms.11123.173182

Abstract:
In this paper, we present results of $\omega$-order preserving partial contraction mapping generating a wave equation. We use the theory of semigroup to generate a wave equation by showing that the operator $ \begin{pmatrix} 0 & I\\ \Delta & 0 \end{pmatrix}, $ which is $A,$ is the infinitesimal generator of a $C_0$-semigroup of operators in some appropriately chosen Banach of functions. Furthermore we show that the operator $A$ is closed, unique and that operator $A$ is the infinitesimal generator of a wave equation.
Merve Esra Türkay
Published: 26 September 2022
Earthline Journal of Mathematical Sciences, Volume 11, pp 145-172; https://doi.org/10.34198/ejms.11123.145172

Abstract:
$q$-Calculus Theory is rapidly growing in various directions. The goal of this paper is to collect and underline recent results on $\alpha q$-analogs of the Cesàro matrix andemphasize various generalizations. One $\alpha q$-analogs of the Cesàro matrix of order one is the triangular matrix with nonzero entries $c_{nk}^{\alpha }\left( q\right) =\tfrac{\left( \alpha q\right) ^{n-k}}{1+q+\cdots +q^{n}},\ 0\leq k\leq n$, where $\alpha ,q\in \left( 0,1\right) $. The purpose of this article examines various spectral decompositions of $C_{q}^{\alpha }=\left( c_{nk}^{\alpha }\left( q\right) \right) $ such as the spectrum, the fine spectrum, the approximate point spectrum, the defect spectrum, and the compression spectrum on the sequence space $c$.
Christian John Etwire, Ibrahim Yakubu Seini, Rabiu Musah, Oluwole Daniel Makinde
Published: 14 September 2022
Earthline Journal of Mathematical Sciences, Volume 11, pp 115-143; https://doi.org/10.34198/ejms.11123.115143

Abstract:
The effects of fluctuating temperature on Darcy-Forchheimer flow of oil-based nanofluid with activation energy and velocity slip has been analyzed. Similarity transformation was used to transform the governing partial differential equations into coupled nonlinear ordinary differential equations and solved numerically with the aid of the fourth order Runge-Kutta algorithm with a shooting technique. Results for the embedded parameters controlling the flow dynamics have been tabulated and illustrated graphically. The slip velocity parameter was found to enhance the Nusselt number but depleted both the skin friction coefficient and Sherwood number while the local inertial was noted to increase both the skin friction coefficient and Sherwood number but diminishes the Nusselt number. These results indicate that the velocity slip parameter and local inertial coefficient can be used to control flow characteristics in industrial and engineering systems.
Yüksel Soykan
Published: 9 September 2022
Earthline Journal of Mathematical Sciences, Volume 11, pp 23-114; https://doi.org/10.34198/ejms.11123.23114

Abstract:
In this paper, we investigate the generalized Fibonacci (Horadam) polynomials and we deal with, in detail, two special cases which we call them $(r,s)$-Fibonacci and $(r,s)$-Lucas polynomials. We present Binet's formulas, generating functions, Simson's formulas, and the summation formulas for these polynomial sequences. Moreover, we give some identities and matrices associated with these sequences. Finally, we present several expressions and combinatorial results of the generalized Fibonacci polynomials.
Innocent U. Akata, Festus C. Opone, Francis E. U. Osagiede
Published: 8 September 2022
Earthline Journal of Mathematical Sciences, Volume 11, pp 1-22; https://doi.org/10.34198/ejms.11123.122

Abstract:
This paper presents a new generalized bounded distribution called the Kumaraswamy unit-Gompertz (KUG) distribution. Some of the Mathematical properties which include; the density function, cumulative distribution function, survival and hazard rate functions, quantile, mode, median, moment, moment generating function, Renyi entropy and distribution of order statistics are derived. We employ the maximum likelihood estimation method to estimate the unknown parameters of the proposed KUG distribution. A Monte Carlo simulation study is carried out to investigate the performance of the maximum likelihood estimates of the unknown parameters of the proposed distribution. Two real datasets are used to illustrate the applicability of the proposed KUG distribution in lifetime data analysis.
Gbeminiyi M. Sobamowo
Published: 7 September 2022
Earthline Journal of Mathematical Sciences, Volume 10, pp 439-456; https://doi.org/10.34198/ejms.10222.439456

Abstract:
In this work, Black-Scholes differential equation for barrier/traditional option is solved using partial Taylor series expansion method. The developed solutions are in very good agreement with the closed-form solutions of the Black Scholes equation for the powered ML-payoff functions. Also, the analytical solutions of the new method in this present study give the same expressions as the solutions of projected differential equations and homotopy perturbation method as presented in the literature. Moreover, the reliability, speed, accuracy, and ease of application of the proposed method show its potential for wide areas of applications in science, financial mathematics, and engineering.
Ayokunle John Tadema, Ebenezer Olayinka Adeniyi
Published: 1 September 2022
Earthline Journal of Mathematical Sciences, Volume 10, pp 423-438; https://doi.org/10.34198/ejms.10222.423438

Abstract:
This study employed Lyapunov function method to investigate the stability of nonlinear ordinary differential equations. Using Lyapunov direct method, we constructed Lyapunov function to investigate the stability of sixth order nonlinear ordinary differential equations. We find $ V(x) $, a quadratic form, positive definite and $ U(x) $ which is also positive definite was chosen such that the derivative of $ V(x) $ with respect to time was equal to the negative value of $ U(x) $.
J. B. Omosowon, A. Y. Akinyele, B. M. Ahmed, O. Y. Saka-Balogun
Earthline Journal of Mathematical Sciences, Volume 10, pp 409-421; https://doi.org/10.34198/ejms.10222.409421

Abstract:
In this paper, results of $\omega$-order preserving partial contraction mapping generating a quasilinear equation of evolution were presented. In general, the study of quasilinear initial value problems is quite complicated. For the sake of simplicity we restricted this study to the mild solution of the initial value problem of a quasilinear equation of evolution. We show that if the problem has a unique mild solution $v\in C([0,T]: X)$ for every given $u\in C([0,T]:X)$, then it defines a mapping $u\to v=F(u)$ of $C([0,T]:X)$ into itself. We also show that under the suitable condition, there exists always a $T',\ 0<T'\leq T$ such that the restriction of the mapping $F$ to $C([0,T']:X)$ is a contraction which maps some ball of $C([0,t']:X)$ into itself by proving the existence of a local mild solution of the initial value problem.
Christophe Chesneau, Festus C. Opone, Ngozi O. Ubaka
Earthline Journal of Mathematical Sciences, Volume 10, pp 385-407; https://doi.org/10.34198/ejms.10222.385407

Abstract:
Modern applied statistics naturally give rise to the continuous Bernoulli distribution (data fitting, deep learning, computer vision, etc). On the mathematical side, it can be viewed as a one-parameter distribution corresponding to a special exponential distribution restricted to the unit interval. As a matter of fact, manageable extensions of this distribution have great potential in the same fields. In this study, we motivate a transmuted version of the continuous Bernoulli distribution with the goal of analyzing proportional data sets. The feature of the created transmuted continuous Bernoulli distribution is an additional parameter that realizes a linear tradeoff between the min and max of two continuous random variables with the continuous Bernoulli distribution. The standard study process is respected: we derive some mathematical properties of the proposed distribution and adopt the maximum likelihood estimation technique in estimating the unknown parameters involved. A Monte Carlo simulation exercise was conducted to examine and confirm the asymptotic behavior of the obtained estimates. In order to show the applicability of the proposed distribution, three proportional data sets are analyzed and the results obtained are compared with competitive distributions. Empirical findings reveal that the transmuted continuous Bernoulli distribution promises more flexibility in fitting proportional data sets than its competitors.
Timilehin Gideon Shaba, Dere Zainab Olabisi
Earthline Journal of Mathematical Sciences, Volume 10, pp 365-384; https://doi.org/10.34198/ejms.10222.365384

Abstract:
The solutions provided in this work address the classic but still relevant topic of establishing new classes of univalent functions linked to $q$-Chebyshev polynomials and examining coefficient estimates features. Aspects of quantum calculus are also considered in this research to make it more unique and produce more pleasing outcomes. We introduce new classes of univalent functions connected to $q$-Chebyshev polynomials, which generalize certain previously investigated classes. The link among the previously published findings and the current ones are noted. For each of the new classes, estimates for the Taylor-Maclaurin coefficients $|r_2|$ and $|r_3|$ are derived and the much-studied Fekete-Szegö functional.
Alaa Hussein Mohammed
Earthline Journal of Mathematical Sciences, Volume 10, pp 355-364; https://doi.org/10.34198/ejms.10222.355364

Abstract:
In this paper, we introduce a new class of operators on Hilbert space called (f*-Ҩ) quasi binormal operator of order ղ. We study this operator and give some of its properties.
Abbas Kareem Wanas, Hussein Kadhim Radhi
Earthline Journal of Mathematical Sciences, Volume 10, pp 341-353; https://doi.org/10.34198/ejms.10222.341353

Abstract:
In this paper, we determine the necessary and sufficient conditions for the power series f(z) whose coefficients are probabilities of the Borel distribution to be in the family J(p,λ ,α,β,γ) of analytic functions which defined in the open unit disk. We derive a number of important geometric properties, such as, coefficient estimates, integral representation, radii of starlikeness and convexity. Also we discuss the extreme points and neighborhood property for functions belongs to this family.
, Yuanyuan Wang
Earthline Journal of Mathematical Sciences, Volume 10, pp 317-340; https://doi.org/10.34198/ejms.10222.317340

Abstract:
Based on the theory of industrial agglomeration affecting urban innovation, the panel data of 269 prefecture-level cities and above in China from 2011 to 2017 was used to empirically analyze the internal relationship between industrial agglomeration and urban innovation. The study found that overall industrial agglomeration and tertiary industry agglomeration have a significant promotion effect on urban innovation, while the secondary industry agglomeration does not significantly affect urban innovation; The overall industrial agglomeration and tertiary industrial agglomeration of eastern cities, large and medium-sized cities, and high-tech cities have a significant role in promoting urban innovation, while the promotion effects of mid-western cities, small-scale cities, low-tech, and medium-tech cities are not obvious; The secondary industry agglomeration has no significant impact on the innovation of all regional cities, large-scale cities, and cities with medium and high-tech levels, and the secondary industry agglomeration of low-tech cities also hinders urban innovation. However, with the improvement of the city's technological level, the effect of the concentration of secondary industries on urban innovation has gradually increased; Further analysis found that after using the PSM model to eliminate urban system differences, the basic conclusion that industrial agglomeration affects urban innovation is still valid. The secondary industry agglomeration has a threshold effect on urban innovation, and the effect of the secondary industry agglomeration on urban innovation will gradually increase with the increase of the degree of secondary industry agglomeration. It can be seen that China's high-quality secondary industry agglomeration effect has not yet formed. The above findings provide a theoretical basis for the rational formulation of industrial policies to promote urban innovation.
T.O. Aliu, Y.O. Aderinto, K. Issa
Earthline Journal of Mathematical Sciences, Volume 10, pp 305-316; https://doi.org/10.34198/ejms.10222.305316

Abstract:
Several approaches have been advanced for solving transportation problems. The most prominent of them in various text being, North West Corner Rule(NWCR), Least Cost Method(LCM), and Vogel's Approximation Method(VAM). This paper considered three additional corner rules, which are North East Corner Rule(NECR), South West Corner Rule(SWCR) and South East Corner Rule(SECR). Algorithms ware provided for obtaining initial feasible solution to Transportation Problems. Three test examples were considered using the rules. The results revealed that the NECR and SWCR have equal result. While NWCR and SECR also produce the same result. NECR and SWCR however, better minimize transportation cost. The two methods are therefore recommended for use in any business organization requiring shipment of products.
Jude Babatunde Omosowon, Akinola Yussuff Akinyele, K. A. Bello, B. M. Ahmed
Earthline Journal of Mathematical Sciences, Volume 10, pp 289-304; https://doi.org/10.34198/ejms.10222.289304

Abstract:
This paper present results of $\omega$-order preserving partial contraction mapping generating a regular weak*-continuous semigroup. We consider a semigroup on a Banach space $X$ and $B:X^\odot\rightarrow X^*$ is bounded, then the intertwining formula was used to define a semigroup $T^B(t)$ on $X^*$ which extends the perturbed semigroup $T^B_0(t)$ on $X^\odot$ using the variation of constants formula. We also investigated a certain class of weak*-continuous semigroups on dual space $X^*$ which contains both adjoint semigroups and their perturbations by operators $B:X^\odot\rightarrow X^*$.
Ali Mohammed Ramadhan, Najah Ali Jiben Al-Ziadi
Earthline Journal of Mathematical Sciences, Volume 10, pp 271-288; https://doi.org/10.34198/ejms.10222.271288

Abstract:
In the present paper, we define a new class NA(n,p,λ,α,β) of multivalent functions which are holomorphic in the unit disk ∆ ={s∈C∶|s|<1}. A necessary and sufficient condition for functions to be in the class NA(n,p,λ,α,β) is obtained. Also, we get some geometric properties like radii of starlikeness, convexity and close-to-convexity, closure theorems, extreme points, integral means inequalities and integral operators.
Christian John Etwire, Ibrahim Yakubu Seini, Oluwole Daniel Makinde
Earthline Journal of Mathematical Sciences, Volume 10, pp 241-270; https://doi.org/10.34198/ejms.10222.241270

Abstract:
Effects of thermal stratification on magnetized flow of electrically induced Maxwell nanofluid over reactive stretching plate have been analyzed. The nonlinear ordinary differential equations governing the flow problem were obtained by applying Similarity transformation. The resulting model was then solved with the aid of the fourth order Runge-Kutta algorithm along with the shooting technique. Results for pertinent flow parameters were tabulated and analyzed graphically. The Richardson number was noted to appreciate the momentum boundary layer thickness but it decayed both the thermal and solutal boundary layer thicknesses.
Ali Mohammed Ramadhan, Najah Ali Jiben Al-Ziadi
Earthline Journal of Mathematical Sciences, Volume 10, pp 227-239; https://doi.org/10.34198/ejms.10222.227239

Abstract:
In the present paper, we investigate two new subclasses 〖AR〗_(Σ_m ) (δ,λ;α) and 〖AR〗_(Σ_m ) (δ,λ;β) of Σ_m consisting of m-fold symmetric holomorphic bi-univalent functions in the open unit disk Δ. For functions from the two classes described here, we obtain estimates on the initial bounds |d_(m+1) | and |d_(2m+1) |. In addition, we get new special cases for our results.
Ayotunde Olajide Lasode
Earthline Journal of Mathematical Sciences, Volume 10, pp 211-225; https://doi.org/10.34198/ejms.10222.211225

Abstract:
By making use of $q$-derivative and $q$-integral operators, we define a class of analytic and bi-univalent functions in the unit disk $|z|<1$. Subsequently, we investigate some properties such as some early coefficient estimates and then obtain the Fekete-Szeg\"o inequality for both real and complex parameters. Further, some interesting corollaries are discussed.
Sahar Jaafar Mahmood
Earthline Journal of Mathematical Sciences, Volume 10, pp 183-193; https://doi.org/10.34198/ejms.10122.183193

Abstract:
This paper contains two directions of work. The first one gives material related to free action (an inner derivation) mappings on a group ring R[G] which is a construction involving a group G and a ring R and the dependent elements related to those mappings in R[G]. The other direction deals with a generalization of the definition of dependent elements and free actions. We concentrate our study on dependent elements, free action mappings and those which satisfy T(x)γ=δx,x∈R[G] and some fixed γ,δ∈R[G]. In the first part we work with one dependent element. In other words, there exists an element γ∈R[G] such that T(x)γ=γx,x∈R[G]. In second one, we characterize the two elements γ,δ∈R[G] which have the property T(x)γ=δx,x∈R[G] and some fixed γ,δ∈R[G], when T is assumed to have additional properties like generalized a derivation mappings.
Brice Réné Amougou Mbarga
Earthline Journal of Mathematical Sciences, Volume 10, pp 169-181; https://doi.org/10.34198/ejms.10122.169181

Abstract:
Over the past years various authors have investigated the famous elementary result in group theory called Goursat's lemma for characterizing the subgroups of the direct product $A\times B$ of two groups $A,B$. Given a homomorphic relation $\rho = (R,A,B)$ where $A$ and $B$ are groups and $R$ is a subgroup of $A\times B.$ What can one say about the structure of $\rho$. In 1950 Riguet proved a theorem that allows us to obtain a characterization of $\rho$ induces by examining the sections of the direct factors. The purpose of this paper is two-fold. A first and more concrete aim is to provide a containment relation property between homomorphic relation. Indeed if $\rho,\sigma$ are homomorphic relations, we provide necessary and sufficient conditions for $\sigma\leq\rho$. A second and more abstract aim is to introduce a generalization of some notions in homological algebra. We define the concepts of $\theta$-exact. We also obtain some interesting results. We use these results to find a generalization of Lambek Lemma.
S. E. Ogunfeyitimi, M. N. O. Ikhile
Earthline Journal of Mathematical Sciences, Volume 10, pp 125-168; https://doi.org/10.34198/ejms.10122.125168

Abstract:
In this paper, we present a new family of multi-block boundary value integration methods based on the Enright second derivative type-methods for differential equations. We rigorously show that this class of multi-block methods are generally $A_{k_1,k_2}$-stable for all block number by verifying through employing the Wiener-Hopf factorization of a matrix polynomial to determine the root distribution of the stability polynomial. Further more, the correct implementation procedure is as well determine by Wiener-Hopf factorization. Some numerical results are presented and a comparison is made with some existing methods. The new methods which output multi-block of solutions of the ordinary differential equations on application, and are unlike the conventional linear multistep methods which output a solution at a point or the conventional boundary value methods and multi-block methods which output a block of solutions per step. The second derivative multi-block boundary value integration methods are a new approach at obtaining very large scale integration methods for the numerical solution of differential equations.
Inci Ege
Earthline Journal of Mathematical Sciences, Volume 10, pp 109-123; https://doi.org/10.34198/ejms.10122.109123

Abstract:
In this paper, some properties for the v-analogue of Gamma and digamma functions are investigated. Also, a celebrated Bohr-Mollerup type theorem related to the v-analogue of Gamma function is given. Furthermore, an expression for the v-digamma function is presented by using the v-analogue of beta function. Also, some limits for the v-analogue of Gamma and beta functions are given.
Akinola Yussuff Akinyele Akinyele, Omotoni Ezekiel Jimoh, Jude Babatunde Omosowon, Kareem Akanbi Bello
Earthline Journal of Mathematical Sciences, Volume 10, pp 97-108; https://doi.org/10.34198/ejms.10122.97108

Abstract:
In this paper, we present results of $\omega$-order preserving partial contraction mapping creating a continuous time Markov semigroup. We use Markov and irreducible operators and their integer powers to describe the evolution of a random system whose state changes at integer times, or whose state is only inspected at integer times. We concluded that a linear operator $P:\ell^{1}(X_+)\rightarrow \ell^{1}(X_+)$ is a Markov operator if its matrix satisfies $P_{x,y}\geqslant 0$ and $\sum_{x\in X_+}P_{x,y=1}$ for all $y\in X$.
Zainab Aodeh A. Mohammed
Earthline Journal of Mathematical Sciences, Volume 10, pp 85-96; https://doi.org/10.34198/ejms.10122.8596

Abstract:
The object of the present paper is to introduce the concept of δ-scattered spaces as a natural generalization of the concept of scattered spaces. We prove that the concept of δ-scatteredness of the space coincides with scatteredness. It is noted that scattered need not be δ-scattered in general, also I-space are comparable with δ-scattered space. We start out by giving a characterization of δ-scattered spaces. We study relationships between δ-scatteredness and with scattered, semi-scattered, α-scattered, sub maximal, irresolvable and N-scattered.
Muhammad Aslam Noor, Hayat Ali, Khalida Inayat Noor
Earthline Journal of Mathematical Sciences, Volume 10, pp 67-84; https://doi.org/10.34198/ejms.10122.6784

Abstract:
Some new types of equilibrium variational-like inequalities are considered, which is called the bifunction mixed equilibrium variational-like inequalities. The auxiliary principle technique is used to construct some iterative schemes to solve these new equilibrium variational-like inequalities. Convergence of the suggested schemes is discussed under relaxed conditions. Several special cases are discussed as applications of the main results. The ideas and techniques may be starting point for future research.
Muhammad Aslam Noor, Khalida Inayat Noor
Earthline Journal of Mathematical Sciences pp 1-66; https://doi.org/10.34198/ejms.10122.166

Abstract:
Quasi variational inequalities can be viewed as novel generalizations of the variational inequalities and variational principles, the origin of which can be traced back to Euler, Lagrange, Newton and Bernoulli's brothers. It is well known that quasi-variational inequalities are equivalent to the implicit fixed point problems. We consider this alternative equivalent fixed point formulation to suggest some new iterative methods for solving quasi-variational inequalities and related optimization problems using projection methods, Wiener-Hopf equations, dynamical systems, merit function and nonexpansive mappings. Convergence analysis of these methods is investigated under suitable conditions. Our results present a significant improvement of previously known methods for solving quasi variational inequalities and related optimization problems. Since the quasi variational inequalities include variational inequalities and complementarity problems as special cases. Results obtained in this paper continue to hold for these problems. Some special cases are discussed as applications of the main results. The implementation of these algorithms and comparison with other methods need further efforts.
O.E. Opaleye, S.O. Fawale, P.O. Awoleye, S. Sunday
Earthline Journal of Mathematical Sciences, Volume 9, pp 265-277; https://doi.org/10.34198/ejms.9222.265277

Abstract:
Basic properties of probability with Poisson distribution is used in obtaining the coefficient bound by subordination principle which is the fundamental purpose of this work. A class of analytic function $f:\xi \rightarrow \mathbb{C}$ with unit disc $\xi :\{z\in\mathbb{C}:|z|<1\}$ is established. Likewise known results of Fekete-Szegö inequalities type and the second bound of Toeplitz determinant are obtained.
O. Beolumn, K. O. Muka
Earthline Journal of Mathematical Sciences, Volume 9, pp 249-264; https://doi.org/10.34198/ejms.9222.249264

Abstract:
Circumventing order restrictions on numerical methods designed for the integration of stiff initial value problem is the concern here via Boundary Value Method. The attainable order p = k+v and linear stability properties of the methods are discussed. The numerical test on some stiff problems shows that the new methods developed, compare favourably with existing methods, with ODE15s of MATLAB used as reference numerical solution.
Mohammed Muniru Iddrisu
Earthline Journal of Mathematical Sciences, Volume 9, pp 237-247; https://doi.org/10.34198/ejms.9222.237247

Abstract:
This paper presents Opial and Steffensen inequalities and also discussed q and (p,q)-calculus. Methods of convexity, (p,q)-differentiability and monotonicity of functions were employed in the analyses and new results related to the Opial's-type inequalities were established.
Alaa Hussein Mohammed
Earthline Journal of Mathematical Sciences, Volume 9, pp 229-235; https://doi.org/10.34198/ejms.9222.229235

Abstract:
In this paper we introduce an operator on Hilbert space H called P^*-skew-bi-normal operator. An operator L is called P^*-skew-bi-normal operator if and only if (L^* LLL^* ) 〖〖(L〗^*)〗^P=〖〖(L〗^*)〗^P (〖LL〗^* L^* L), where Ρ is a nonnegative integer. New theorems and properties are given on Hilbert space H.
Festus C. Opone, Joseph E. Osemwenkhae
Earthline Journal of Mathematical Sciences, Volume 9, pp 179-199; https://doi.org/10.34198/ejms.9222.179199

Abstract:
In this paper, we introduced an extension of the Marshall-Olkin Extended Topp-Leone distribution using the quadratic rank transmutation map (QRTM). Statistical properties of the proposed distribution are examined and its parameter estimates are obtained using the maximum likelihood method. A real data set defined on a unit interval is employed to illustrate the usefulness of the proposed distribution among existing distributions with bounded support.
Salvatore Mazzullo
Earthline Journal of Mathematical Sciences, Volume 9, pp 201-227; https://doi.org/10.34198/ejms.9222.201227

Abstract:
We will use the definition of entropy to calculate the Earth annual and millennial temperature profile having the highest probability among all probable temperature profiles. We will achieve this through the development of an original procedure for identifying the physical parameters of a paleo-climatic model of the Earth. This investigation will allow us to answer two questions of contemporary experimental and theoretical research: The first concerns the increase in sea temperature and the Earth accumulation of heat, measured in the last sixty years. The second concerns the probability of two events of capital interest for humanity: the onset of an ice age and the onset of a climatic optimum. This paleo-climatic model provides the answer that the probability of the onset of an ice age is higher than the advent of a climatic optimum within an interglacial period.
Hasan Bayram, Sibel Yalçın
Earthline Journal of Mathematical Sciences, Volume 9, pp 165-178; https://doi.org/10.34198/ejms.9222.165178

Abstract:
We introduce and investigate q-analogue of a new subclass of Salagean-type harmonic univalent functions defined by subordination. We first obtained a coefficient characterization of these functions. We give necessary and sufficient convolution conditions, distortion bounds, compactness and extreme points for this subclass of harmonic univalent functions with negative coefficients.
Archit Chaturvedi
Earthline Journal of Mathematical Sciences pp 131-143; https://doi.org/10.34198/ejms.9122.131143

Abstract:
Polymers are an essential aspect of molecular biology and biochemistry. The most significant of macromolecules involved in biological processes and phenomena are polymers. In this article, we provide a comprehensive summary of the proposed physical models for the configuration of polymers. Such physical models include the freely-jointed chain, freely-rotating chain, worm-like chain, and the Gaussian chain model. We then connect these models to the existing models regarding the radiation biophysics of DNA damage, as well as to the damage of RNA molecules, and provide an insight into future areas of research in the subject areas. The conclusion is that polymer physics and the Linear-Quadratic model can be used for future biophysical research in cancer and neurological disorders. Through such connections, we hope to provide a potential future insight with regards to biophysical research in cancer and neurodegenerative disorders.
Muhammad Aslam Noor, Khalida Inayat Noor
Earthline Journal of Mathematical Sciences, Volume 9, pp 145-164; https://doi.org/10.34198/ejms.9222.145164

Abstract:
In this paper, we introduce a new class of variational inclusions involving three operators. We suggest and analyze three-step iterations for finding the common element of the set of fixed points of a nonexpansive mappings and the set of the solutions of the variational inclusions using the resolvent operator technique. We also study the convergence criteria of three-step iterative method under some mild conditions. Inertial type methods are suggested and investigated for general variational inclusions. Our results include the previous results as special cases and may be considered as an improvement and refinement of the previously known results.
Abbas Kareem Wanas, Noor Jassim Hammadi
Earthline Journal of Mathematical Sciences pp 117-129; https://doi.org/10.34198/ejms.9122.117129

Abstract:
The purpose of this work is to use fractional integral and Wanas operator to define a certain class of analytic and univalent functions defined in the open unit disk U. Also, we obtain some results for this class such as integral representation, inclusion relationship and argument estimate.
Abbas Kareem Wanas, Hussein Mohammed Ahsoni
Earthline Journal of Mathematical Sciences pp 105-116; https://doi.org/10.34198/ejms.9122.105116

Abstract:
In the present paper, we introduce and study a subclass of analytic and univalent functions associated with Beta negative binomial distribution series which is defined in the open unit disk U. We discuss some important geometric properties of this subclass, like, coefficient estimates, extreme points and integral representation. Also, we obtain results about integral mean associated with fractional integral.
Muqadssa Shahzadi
Earthline Journal of Mathematical Sciences, Volume 9, pp 79-91; https://doi.org/10.34198/ejms.9122.7991

Abstract:
Some iterative algorithms for solving nonlinear equation $f(x) = 0$ are suggested and investigated using Taylor series and homotopy perturbation technique. These algorithms can be viewed as extensions and generalization of well known methods such as Householder and Halley methods with cubic convergence. Convergence of the proposed methods has been discussed and analyzed. Several numerical examples are given to illustrate the efficiency of the suggested algorithms for solving nonlinear equations. Comparison with other iterative schemes is carried out to show the validity and performance of these algorithms.
Alaa Hussein Mohammed
Published: 16 February 2022
Earthline Journal of Mathematical Sciences, Volume 8, pp 337-342; https://doi.org/10.34198/ejms.8222.337342

Abstract:
In this paper we introduce a new class of operators on Hilbert space called q-power quasi binormal operator. We study this operator and give some properties of it.
Jayeola Dare, Aye O. Patrick, David O. Oyewola
Published: 16 February 2022
Earthline Journal of Mathematical Sciences, Volume 8, pp 325-336; https://doi.org/10.34198/ejms.8222.325336

Abstract:
The movements in Asset prices are very complex, therefore seem to be unpredictable. However, one of the main challenges of the econometric models is to get the best data for forecasting in order to present accurate results. This paper investigates the performance of stationary and non-stationary data on Ljung Box test statistics, to check the fitness of the data for forecasting. In the paper three assets (Groundnut, sorghum and soya bean) are used, tests are conducted for Ljung box statistics; Correlogram, Histogram Normality and Heteroscedasticity test. It is observed that stationary data are better for forecasting than non-stationary data in this research.
Patrick O. Aye, D. Jayeola, David O. Oyewola
Published: 16 February 2022
Earthline Journal of Mathematical Sciences, Volume 8, pp 313-324; https://doi.org/10.34198/ejms.8222.313324

Abstract:
This study employed Lyapunov function method to examine the stability of nonlinear ordinary differential equations. Using direct Lyapunov method, we constructed Lyapunov function to investigate the stability of fifth order nonlinear ordinary differential equations. V(x), a quadratic form and positive definite and U(x) which is also positive definite was chosen such that the derivative of V(x) with respect to time would be equal to the negative value of U(x). We adopted the pre-multiplication of the given equation by x..... and obtained a Lyapunov function which established local and global stability of a fifth order differential equation.
Anthony Joe Turkson
Published: 25 February 2022
Earthline Journal of Mathematical Sciences, Volume 9, pp 53-77; https://doi.org/10.34198/ejms.9122.5377

Abstract:
In reliability analysis, both the Weibull and the lognormal distributions could be analyzed using the observed data logarithms. While the Weibull data logarithm is skewed, the lognormal data logarithm is symmetrical. This review work initiates discussions on and syntheses of the various views held on the use of the frequentist and Bayesian approaches to drawing statistical inferences on failure time distributions of survival models. Of greater concern was the discussion on the use of the exponential, Weibull and log-normal distributions in reliability analysis. Various methods have been used to discriminate between the two most important distributions. They include: Coefficients of variation (CV); the standard deviation of the data logarithms (SD); the percentile position of the mean of the data logarithm (PP); the cumulated logarithm dispersion before and after the mean (CLD); ratio of the maximum likelihood (RML); Kullback-Leibler Divergence (KLD); and Minimized Kullback-Leibler Divergence (RMKLD). In the (CV, SD, PP and CLD) study, a stress-strength data set was used for the analysis. The stress data followed a lognormal distribution, while the strength data followed a Weibull distribution, therefore for the stress-strength analysis the lognormal-Weibull combination was used. In the ratio of the maximum likelihood (RML) study, it was averred that though each of the distributions had great applications, none of them produced a good fit. In the study using Kullback-Leibler Divergence (KLD); and Minimized Kullback-Leibler Divergence (RMKLD), test results revealed that RML=0.345>0. Hence the lognormal distribution was selected. Similarly, the RMKLD=0.6028>0, therefore the Weibull distribution was selected. In the final analysis, none of the study results could reject the Weibull in favour of the lognormal distribution model. In respect of the frequentist and the Bayesian approach to conducting statistical inferences, it came out strongly that it was high time psychologist who had adopted the use of the frequentist framework moved away from it and started using the Bayesian approach. A shift towards the use of the Bayesian, lognormal-Weibull approach is thus recommendable.
Chinwe N. Obi
Published: 16 February 2022
Earthline Journal of Mathematical Sciences, Volume 8, pp 305-312; https://doi.org/10.34198/ejms.8222.305312

Abstract:
This paper focuses on finding the solution of some nonlinear partial differential equations with initial and boundary conditions. This is achieved using the homotopy perturbation method. The solutions obtained are said to be analytic approximate in nature. The applications basically are on inhomogeneous partial differential equations.
Zainab Aodeh A. Mohammed
Published: 20 February 2022
Earthline Journal of Mathematical Sciences, Volume 9, pp 41-51; https://doi.org/10.34198/ejms.9122.4151

Abstract:
Sharp bounds for the Fekete-Szegö functional |ν_1-ξ〖ν_0〗^2 | are derived for certain class of meromorphic starlike functions ω(z) of order β defined on the punctured open unit disk for which 1-1/t ((D^(n+1˳m) ω(z))/(D^(n˳m) ω(z) )-1)≺χ(z) (t∈C-{0},η≥0,κ>0,n,m∈N_0), lie in a region starlike with respect to 1 and symmetric with respect to the real axis.
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