A New Variant of Symmetric Distance Spaces and an Extension of the Banach Fixed-Point Theorem

Abstract

The notion of $\mathrm{\Delta }$ -metric spaces has been proposed in this study as a generalization of $b$ -metric spaces, extended $b$ -metric spaces, and $p$ -metric spaces. A number of topological characteristics of such spaces have been investigated in this paper. On such spaces, a noncompactness measure has been established, and some results in the framework of noncompactness measure have been achieved. We prove an analogous of the Banach contraction principle in such spaces based on this approach. In order to investigate the validity of the underlying space and our proven fixed-point theorems, supporting examples have been presented. Furthermore, the well-posedness of the fixed-point problem has been tested using our fixed-point result.