Abstract and Applied Analysis
ISSN / EISSN : 1085-3375 / 1687-0409
Published by: Hindawi Limited (10.1155)
Total articles ≅ 5,414
Latest articles in this journal
Abstract and Applied Analysis, Volume 2021, pp 1-12; https://doi.org/10.1155/2021/8624794
In this work, we consider the Darboux frame T , V , U of a curve lying on an arbitrary regular surface and we construct ruled surfaces having a base curve which is a V -direction curve. Subsequently, a detailed study of these surfaces is made in the case where the directing vector of their generatrices is a vector of the Darboux frame, a Darboux vector field. Finally, we give some examples for special curves such as the asymptotic line, geodesic curve, and principal line, with illustrations of the different cases studied.
Abstract and Applied Analysis, Volume 2021, pp 1-8; https://doi.org/10.1155/2021/9959374
We present the concept of α , k , θ , φ -contractive multivalued mappings in b -metric spaces and prove some fixed point results for these mappings in this study. Our results expand and refine some of the literature’s findings in fixed point theory.
Abstract and Applied Analysis, Volume 2021, pp 1-9; https://doi.org/10.1155/2021/3151501
In this paper, we introduce original definitions of Partner ruled surfaces according to the Darboux frame of a curve lying on an arbitrary regular surface in E 3 . It concerns T g Partner ruled surfaces, T n Partner ruled surfaces, and g n Partner ruled surfaces. We aim to study the simultaneous developability conditions of each couple of two Partner ruled surfaces. Finally, we give an illustrative example for our study.
Abstract and Applied Analysis, Volume 2021, pp 1-7; https://doi.org/10.1155/2021/2298192
In this paper, we consider a source problem for a time harmonic acoustic wave in two-dimensional space. Based on the boundary integral equation method, a Dirichlet-to-Neumann map in terms of boundary integral operators on the boundary of the source is constructed to transform this problem into two boundary value problems for the Helmholtz equation.
Abstract and Applied Analysis, Volume 2021, pp 1-10; https://doi.org/10.1155/2021/4846877
In this article, we propose two Banach-type fixed point theorems on bipolar metric spaces. More specifically, we look at covariant maps between bipolar metric spaces and consider iterates of the map involved. We also propose a generalization of the Banach fixed point result via Caristi-type arguments.
Abstract and Applied Analysis, Volume 2021, pp 1-10; https://doi.org/10.1155/2021/9961013
In the present paper, we establish some composition formulas for Marichev-Saigo-Maeda (MSM) fractional calculus operators with V -function as the kernel. In addition, on account of V -function, a variety of known results associated with special functions such as the Mittag-Leffler function, exponential function, Struve’s function, Lommel’s function, the Bessel function, Wright’s generalized Bessel function, and the generalized hypergeometric function have been discovered by defining suitable values for the parameters.
Abstract and Applied Analysis, Volume 2021, pp 1-13; https://doi.org/10.1155/2021/5517215
Let A and B be two closed linear relations acting between two Banach spaces X and Y , and let λ be a complex number. We study the stability of the nullity and deficiency of A when it is perturbed by λ B . In particular, we show the existence of a constant ρ > 0 for which both the nullity and deficiency of A remain stable under perturbation by λ B for all λ inside the disk λ < ρ .
Abstract and Applied Analysis, Volume 2021, pp 1-13; https://doi.org/10.1155/2021/2861194
S. A method for the group classification of differential equations is proposed. It is based on the determination of all possible cases of linear dependence of certain indeterminates appearing in the determining equations of symmetries of the equation. The method is simple and systematic and applied to a family of hyperbolic equations. Moreover, as the given family contains several known equations with important physical applications, low-order conservation laws of some relevant equations from the family are computed, and the results obtained are discussed with regard to the symmetry integrability of a particular class from the underlying family of hyperbolic equations.
Abstract and Applied Analysis, Volume 2021, pp 1-8; https://doi.org/10.1155/2021/5556275
The main goal of this paper is to investigate the boundedness and essential norm of a class of product-type operators T u , v , φ m , m ∈ ℕ from Hardy spaces into n th weighted-type spaces. As a corollary, we obtain some equivalent conditions for compactness of such operators.
Abstract and Applied Analysis, Volume 2021, pp 1-5; https://doi.org/10.1155/2021/9951815
In this article, small modification to the Modified Euler Method is proposed. Stability and consistency were tested to determine the end result, and some numerical results were presented, and the CPU time was compared again, and it is recognized that the proposed method is more reliable and compatible with higher efficiency.