#### Advances in Mathematics: Scientific Journal

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ISSN / EISSN : 1857-8365 / 1857-8438
Total articles ≅ 1,333
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Published: 19 July 2021
Advances in Mathematics: Scientific Journal, Volume 10, pp 2977-2998; doi:10.37418/amsj.10.7.5

Abstract:
In this paper, we present some fixed point results for a generalized class of nonexpansive mappings in the framework of uniformly convex hyperbolic space and also propose a new iterative scheme for approximating the fixed point of this class of mappings in the framework of uniformly convex hyperbolic spaces. Furthermore, we establish some basic properties and some strong and $\triangle$-convergence theorems for these mappings in uniformly convex hyperbolic spaces. Finally, we present an application to the nonlinear integral equation and also, a numerical example to illustrate our main result and then display the efficiency of the proposed algorithm compared to different iterative algorithms in the literature with different choices of parameters and initial guesses. The results obtained in this paper extends and generalizes corresponding results in uniformly convex Banach spaces, CAT(0) spaces and other related results in literature.
A. Akpolile, E. Mokobia, J. Ikubor
Published: 16 July 2021
Advances in Mathematics: Scientific Journal, Volume 10, pp 2957-2976; doi:10.37418/amsj.10.7.4

Abstract:
In clinical practice, body temperature is an acclaimed indicator for diagnosis and treatments amongst other follow - ups. This work studied the temperature distribution in deep-seated tissues using Penne’s bio-heat equation (PBE). The analytical solution of the PBE was formulated using the separation of variable technique. The resulting solution gives an expression for tissue temperature in organs that are located inside the body. This revealed that the tissue temperature is subject to changes in tissue thickness, the distance of tissue from the skin surface and other thermal properties of tissues under consideration.
I. Bozorov, U. Shadiev, G. Yodgorov
Published: 10 July 2021
Advances in Mathematics: Scientific Journal, Volume 10, pp 2933-2946; doi:10.37418/amsj.10.7.2

Abstract:
In this paper, we consider the four-particle Schr\"{o}dinger operator corresponding to the Hamiltonian of a system of four arbitrary quantum particles via a three-particle contact interaction potential on a three-dimensional lattice. The finiteness of the number of eigenvalues of the Schr\"{o}dinger operator lying to the left of the essential spectrum for zero value of the total quasi-momentum is proved.
Yaogan Mensah
Published: 10 July 2021
Advances in Mathematics: Scientific Journal, Volume 10, pp 2947-2955; doi:10.37418/amsj.10.7.3

Abstract:
In this paper, we define Sobolev spaces on a locally compact unimodular group in link with the spherical Fourier transform of type $\delta$. Properties of these spaces are obtained. Analogues of Sobolev embedding theorems are proved.
Y. Ahmed, M. Aslam
Published: 4 July 2021
Advances in Mathematics: Scientific Journal, Volume 10, pp 2919-2931; doi:10.37418/amsj.10.7.1

Abstract:
In this article, $Top(X_{n})$ is the collection of all topologies on a given set $X_{n}$ having cardinality $n$. We introduce the method to find the number of topologies of finite sets of cardinality up to $5$ by combinations and counting principles, which enable us to enumerate the classes of homeomorphic disconnected topologies as well as the connected topologies. Moreover we study the graphical aspects of the connected and disconnected topologies.
G. Sheeja, E. Rupavathi
Published: 30 June 2021
Advances in Mathematics: Scientific Journal, Volume 10, pp 2909-2917; doi:10.37418/amsj.10.6.16

Abstract:
In this paper, medical diagnosis concerning isolated systolic hypertension and a study on implication operators is introduced, but fuzzy pentagonal number matrix concepts developed to give a numerical example and graphical representation are also established.
N. Zahra, M. Ibrahim
Published: 24 June 2021
Advances in Mathematics: Scientific Journal, Volume 10, pp 2887-2908; doi:10.37418/amsj.10.6.15

Abstract:
The optical transpose interconnection system (OTIS) arrange has numerous application in designed for equal just as in conveyed arrange. Distinctive interconnection networks has contemplated identified with topological descriptors in [\cite{25,26}]. The present article is a contribution to Ve-degree and Ev-degree base topological indices of biswapped network with premise diagram as path and complete graph. In addition, some delicated recipes are too gotten for various kinds of topological records for the OTIS biswapped network by taking the path and complete graph on $n$ vertices as premise of diagram.
N. Faried, M.S.S. Ali, A.A. Badr
Published: 22 June 2021
Advances in Mathematics: Scientific Journal, Volume 10, pp 2865-2876; doi:10.37418/amsj.10.6.13

Abstract:
The aim of this article is to introduce the definition of the conjugate of sub $E$-functions, which plays an important role in linking the concept of duality among sub $E$-functions. Furthermore, some properties for this class are established.
In this article, the notions of $I_{2}$-localized and $I_{2}^{*}$-localized sequences in metric spaces are defined. Besides, we study some properties associated to $I_{2}$-localized and $I_{2}$-Cauchy sequences. On the other hand, we define the notion of uniformly $I_{2}$-localized sequences in metric spaces.