Ulam–Hyers Stability via Fixed Point Results for Special Contractions in b-Metric Spaces

Abstract

In this paper, we present some fixed point results for Subrahmanyan contraction in the setting of a b-metric space. We consider the case of multivalued operators. We also deduce the Ulam–Hyers stability property of the fixed point inclusion. The notion of b-metric generalizes the one of a metric, as in the third condition, the right-hand side is multiplied by a real number greater than 1. We remark that the second axiom, i.e., the one which shows the symmetry of the b-metric, remains unchanged. The findings presented in this paper extend some recent results which were proved in the context of a metric space. Some open questions are presented at the end of the paper.