Journal of Function Spaces

Let be a nonempty set, be a commutative Banach algebra, and . In this paper, we present a concise proof for the result concerning the BSE (Banach space extension) property of . Specifically, we establish that possesses the BSE property if and only if is finite and is BSE. Additionally, we investigate the BSE module property on Banach -modules and demonstrate that a Banach space serves as a BSE Banach -module if and only if is finite and represents a BSE Banach -module.

In mathematical chemistry, the algebraic polynomial serves as essential for calculating the most accurate expressions of distance-based, degree-distance-based, and degree-based topological indices. The chemical reactivity of molecules, which includes their tendency to engage in particular chemical processes or go through particular reactions, can be predicted using topological indices. Considerable effort has been put into examining the many topological descriptors of simple graphs using ring structures and well-known groups instead of nonassociative algebras, quasigroups, and loops. Both finite quasigroups and loops are the generalizations of groups. In this article, we calculate topological descriptors and some well-known polynomials, -polynomial, Hosoya’s polynomial, Schultz’s polynomial, and modified Schultz polynomial of finite relatively prime graphs of most orders connected with two classes of quasigroups and go through their graphical aspects.

In this paper, the Parseval --frames are constructed from a given --frame by scaling the elements of the --frame with the help of diagonal operators, and these frames are named scalable --frames. Also, we prove some properties of scalable --frames and construct new scalable --frames from a given --frame. The necessary and sufficient conditions for a --frame to be scalable are given. Further, equivalent conditions for the scalability of --frames and the -frames induced by --frames are obtained. Finally, it is shown that the direct sum of two scalable --frames is again a scalable --frame for some suitable bounded linear operator .

The Orlicz function-defined sequence spaces of functions by relative uniform convergence of sequences related to -absolutely summable spaces are a new concept that is introduced in this article. We look at its various attributes, such as solidity, completeness, and symmetry. We also look at a few insertional connections involving these spaces.

The role of iterative algorithms is vital in exploring the diverse domains of science and has proven to be a powerful tool for solving complex computational problems in the most trending branches of computer science. Taking motivation from this fact, we develop and apply a modified four-step iterative algorithm to solve the fixed point problem in the Hadamard spaces using a total asymptotic nonexpansive mapping. MATLAB R2018b is used for numerical experiments to ensure a better convergence rate of the proposed iterative algorithm with existing results.

This article examines the norms of composition operators from the weighted harmonic Bloch space to the weighted harmonic Zygmund space . The critical norm is on the open unit disk. We first give necessary and sufficient conditions where the composition operator between and is bounded. Secondly, we will study the compactness case of the composition operator between and . Finally, we will estimate the essential norms of the composition operator between and .