\(S^{JS}\)-metric spaces: a survey
Authors
I. Beg
- Department of Mathematics and Statistical Sciences, Lahore School of Economics, Lahore 53200, Pakistan.
K. Roy
- Department of Mathematics, Supreme Knowledge Foundation Group of Institutions, Chandannagar, Hooghly-712139, West Bengal, India.
M. Saha
- Department of Mathematics, The University of Burdwan, Purba Bardhaman-713104, West Bengal, India.
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.
Share and Cite
ISRP Style
I. Beg, K. Roy, M. Saha, \(S^{JS}\)-metric spaces: a survey, Journal of Nonlinear Sciences and Applications, 17 (2024), no. 1, 30--69
AMA Style
Beg I., Roy K., Saha M., \(S^{JS}\)-metric spaces: a survey. J. Nonlinear Sci. Appl. (2024); 17(1):30--69
Chicago/Turabian Style
Beg, I., Roy, K., Saha, M.. "\(S^{JS}\)-metric spaces: a survey." Journal of Nonlinear Sciences and Applications, 17, no. 1 (2024): 30--69
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
MSC
- 54E35
- 54E45
- 54A05
- 47H10
- 54D30
- 54H25
- 46S99
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