Nadler and Kannan Type Set Valued Mappings in <i>M</i>-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.

Keywords

• homotopy
• M-metric
• M-Pompeiu–Hausdorff type metric
• multivalued mapping
• fixed point