Nadler and Kannan type set valued mappings in M-metric spaces and an application

Abstract

This article intends to initiate the study of Pompeiu-Hausdorff distance induced by an M-metric. The Nadler and Kannan type fixed point theorems for set-valued mappings are also established in the said spaces. Moreover, the discussion is supported with the aid of competent examples and a result on homotopy. This approach improves the current state of art in fixed point theory.