S J S -metric spaces: a survey

Abstract

The aim of this survey article, is to present in one place the recently published results on S JS -metric spaces, their generalizations and applications. We start with S JS -metric spaces and study their properties. Then we deal with abstract S JS -topological spaces induced by S JS -metric and present several classical results including Cantor's intersection theorem. Next the notion of sequentially compactness on S JS -metric spaces and properties of sequentially compact S JS -metric spaces are studied. Some fixed point theorems are obtained for integral type contractive mappings. Finally we prove several new results on fixed point for rational type contractive mappings, obtain Ekeland's variational principle on S JS -metric spaces as an application and in the end also present results regarding best S JS -proximity point with application.