In this paper, a metric on \(S_b\) -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 \(\mathcal {M}\) is a \(S_b\) metric space. We have presented here the fixed point results for the set-valued map in the framework of \(S_b\) 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 \(S_b\) metric space from the metric space. Illustrative examples and numerical calculations are given to support the obtained results.
