Advances in the study of metric type spaces

Abstract

In this article, we discuss some new fixed point results for self maps defined on a metric type spaces. We also give common fixed point theorems in the same setting.

On Optimal Fuzzy Best Proximity Coincidence Points of Proximal Contractions Involving Cyclic Mappings in Non-Archimedean Fuzzy Metric Spaces

“…There are also abundant studies on all such topics in classical metric spaces and Banach spaces, either in the fuzzy formalism or not necessarily under the fuzzy formalism, including a lot of research on contractive and non-expansive mappings, self-mappings and, in particular, cyclic proximal mappings. (See, for instance, [26][27][28][29][38][39][40][41][42][43] and the references therein concerning different iterative schemes and their relations to proximal split feasibility, variational inequalities and fixed point problems. There are also recent studies on the generalizations of several types of contractions in [31] with an introduction of the so-called simulation function.…”

$η$-metric structures

“…In [7], M. A. Khamsi connected this concept with a generalised form of metric space that he named metric type space (MTS for short). Topological properties of metric type spaces and fixed point theorems for contractive mappings in metric type spaces can extensively be read in [1,4,6,8]. The originality of the work by Huang [9] lies in the fact that they replace the real numbers by an ordered Banach space where the order on the underlying Banach space is defined via an associated cone subset.…”