Some new fixed points results for a class of set-valued mappings in metric spaces

Abstract

In this article, a wider class of set-valued mappings is introduced, and a fixed point theorem for this new mapping in a metric space is proved. Then, we derive a number of implications from our main finding. We also present two non-trivial examples to support our primary theorem. Moreover, we look into fixed point set stability for set-valued mappings and well-posedness. Finally, we present an application to integral inclusion problem.