Journal of Function Spaces

In this paper, we consider the initial boundary value problem for a class of singular parabolic equations with viscoelastic term and logarithmic term. By using the technique of cut-off and the method of Faedo-Galerkin approximation, the local existence of the weak solution is established. Based on the potential well method, the global existence of the weak solution is derived. Furthermore, we prove that the weak solution blows up in finite time by taking the concavity analysis method.

It has been shown that the findings of -metric spaces may be deduced from -metric spaces by considering . In this study, no such concepts that translate to the outcomes of metric spaces are considered. We establish standard fixed point theorems for integral type contractions involving rational terms in the context of complete -metric spaces and discuss their implications. We also provide examples to illustrate the work. This paper’s findings generalize and expand a number of previously published conclusions. In addition, the abstract conclusions are supported by an application of the Riemann-Liouville calculus to a fractional integral problem and a supportive numerical example.

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.