Generalized Hausdorff metric on Sb-metric space and some fixed point results

Abstract

In this paper, a metric on Sb-metric space analogous to the Hausdorff metric has been introduced, and we have proved that the set of all bounded and closed subsets of any non-empty set M is a Sb metric space. We have presented here the fixed point results for the set-valued map in the framework of Sb metric space, which generalizes the famous Nadler’s (Pac J Math 30(2):475–488, 1969) fixed point results for the set-valued map in the metric space. Furthermore, we have generalized Theorem 2 of Kikkawa and Suzuki (Nonlinear Anal Theory Methods Appl 69(9):2942–2949) in the setting of Sb metric space from the metric space. Illustrative examples and numerical calculations are given to support the obtained results. © The Author(s), under exclusive licence to The Forum D’Analystes 2024.