A Mizoguchi-Takahashi type fixed point theorem in complete extended b-metric spaces

Abstract

In this paper, we prove a new fixed point theorem for a multi-valued mapping from a complete extended b-metric space U into the non empty closed and bounded subsets of U, which generalizes Nadler's fixed point theorem. We also establish some fixed point results, which generalize our first result. Furthermore, we establish Mizoguchi-Takahashi's type fixed point theorem for a multi-valued mapping from a complete extended b-metric space U into the non empty closed and bounded subsets of U that improves many existing results in the literature.