$S^{JS}$-metric spaces: a survey

Beg, I.¹ ; Roy, K.² ; Saha, M.³

¹ Department of Mathematics and Statistical Sciences, Lahore School of Economics, Lahore 53200, Pakistan
² Department of Mathematics, Supreme Knowledge Foundation Group of Institutions, Chandannagar, Hooghly-712139, West Bengal, India
³ Department of Mathematics, The University of Burdwan, Purba Bardhaman-713104, West Bengal, India

Journal of nonlinear sciences and its applications, Tome 17 (2024) no. 1, p. 30-69.

Résumé

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.

Détail

DOI : 10.22436/jnsa.017.01.03

Classification : 54E35, 54E45, 54A05, 47H10, 54D30, 54H25, 46S99
Keywords: \(S^{JS}\)-metric space, \(S^{JS}\)-topological space, \(S_{b} \)-metric space, generalized metric, Cantor's intersection property, Ekeland's variational principle, contractive type mapping, \(\mathcal{Z}\)-type contractive map, rational type contractive map, fixed point, \(S^{JS}\)-proximity point

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