Year: 2025
Type: article
Abstract: It is well‐known that the main objective of metric‐like spaces is to pave way for the development of fixed point results in nonstandard framework, such as in nonsymmetric distance structures, where self‐distances might be nonzero. This objective becomes more achievable when the range set of the distance function is a C ∗ ‐algebra. Unfortunately, the idea of the latter is yet to be examined, following the existing literature. Hence, the principal focus of this paper is to introduce the concept of C ∗ ‐algebra‐valued metric‐like space. Thereafter, some topological properties and fixed point theorems in the new space are studied. Comparative examples are provided to show that the proposed ideas herein are new and generalize a few important corresponding results in the literature. From application point of view, new conditions for the existence and uniqueness of a solution to a class of integral equations are established, using one of our obtained theorems.
Source: Journal of Mathematics
DOI: 10.1155/jom/4878114
Authors: Zulaihatu Tijjani Ahmad, Mohammed Shehu Shagari, Maha Noorwali, Abba Ali Tijjani, Afis Saliu
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,160
OpenAlex ID: W4412651508