Some remarks on bv(s)-metric spaces and fixed point results with an application
Articles
Hiranmoy Garai
National Institute of Technology
https://orcid.org/0000-0001-7401-7348
Lakshmi Kanta Dey
National Institute of Technology
https://orcid.org/0000-0001-5389-6048
Pratikshan Mondal
Durgapur Government College
Stojan Radenović
University of Belgrade
Published 2020-11-01
https://doi.org/10.15388/namc.2020.25.20559
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Keywords

boundedly compact space
sequentially compact space
contractive mapping
bv(s)-metric spaces

How to Cite

Garai H., Dey L. K., Mondal P. and Radenović S. (2020) “Some remarks on bv(s)-metric spaces and fixed point results with an application”, Nonlinear Analysis: Modelling and Control, 25(6), pp. 1015-1034. doi: 10.15388/namc.2020.25.20559.

Abstract

We compare the newly defined bv(s)-metric spaces with several other abstract spaces like metric spaces, b-metric spaces and show that some well-known results, which hold in the latter class of spaces, may not hold in bv(s)-metric spaces. Besides, we introduce the notions of sequential compactness and bounded compactness in the framework of bv(s)-metric spaces. Using these notions, we prove some fixed point results involving Nemytzki–Edelstein type mappings in this setting, from which several comparable fixed point results can be deduced. In addition to these, we find some existence and uniqueness criteria for the solution to a certain type of mixed Fredholm–Volterra integral equations.

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