A generalization of set-valued Prešić–Reich type contractions in ultrametric spaces with applications

Abstract

In this paper, we study the existence and uniqueness of coincidence and common fixed point of a set-valued and a single-valued mapping satisfying generalized set-valued Presic–Reich type contractive condition in ultrametric spaces without the property of completeness. As an application, the well-posedness of a common fixed point problem is proved. An example is given to illustrate our results. Our results generalize and extend the results of Presic–Reich in the context of ultrametric spaces.