On parametric \(S\)-metric spaces and fixed-point type theorems for expansive mappings (Q670583)

Summary: 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.