Journal of Nonlinear Sciences and Applications. JNSA (J. Nonlinear Sci. Appl.) (20240101), 17, no.~1, 30-69. ISSN: 2008-1898 (print).eISSN: 2008-1901.
Subject
46 Functional analysis -- 46S Other 46S99 None of the above, but in this section
47 Operator theory -- 47H Nonlinear operators and their properties 47H10 Fixed-point theorems
54 General topology -- 54A Generalities 54A05 Topological spaces and generalizations
54 General topology -- 54D Fairly general properties 54D30 Compactness
54 General topology -- 54E Spaces with richer structures 54E45 Compact
54 General topology -- 54H Connections with other structures, applications 54H25 Fixed-point and coincidence theorems
Language
English
Online Access
초록
Summary: ``The aim of this survey article, is to present in one place the recently published results on ${\rm S^{JS}}$-metric spaces, their generalizations and applications. We start with ${\rm S^{JS}}$-metric spaces and study their properties. Then we deal with abstract ${\rm S^{JS}}$-topological spaces induced by ${\rm S^{JS}}$-metric and present several classical results including Cantor's intersection theorem. Next the notion of sequentially compactness on ${\rm S^{JS}}$-metric spaces and properties of sequentially compact ${\rm S^{JS}}$-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 ${\rm S^{JS}}$-metric spaces as an application and in the end also present results regarding best ${\rm S^{JS}}$-proximity point with application.''