On Parametric S-Metric Spaces and Fixed-Point Type Theorems for Expansive Mappings

Abstract

We introduce the notion of a parametric S-metric space as generalization of a parametric metric space. Using some expansive mappings, we prove a fixed-point theorem on a parametric S-metric space. It is important to obtain new fixed-point theorems on a parametric S-metric space because there exist some parametric S-metrics which are not generated by any parametric metric. We expect that many mathematicians will study various fixed-point theorems using new expansive mappings (or contractive mappings) in a parametric S-metric space.