The meir-keeler type contractions in extended modular b-metric spaces with an application

Abstract

In this paper, we introduce the notion of a modular p-metric space (an extended modular b-metric space) and establish some fixed point results for α-v-Meir-Keeler contractions in this new space. Using these results, we deduce some new fixed point theorems in extended modular metric spaces endowed with a graph and in partially ordered extended modular metric spaces. Also, we develop an important relation between fuzzy-Meir-Keeler and extended fuzzy p-metric with modular p-metric and get certain new fixed point results in triangular fuzzy p-metric spaces. We provide an example and an application to support our results which generalize several well known results in the literature.