The Meir-Keeler type contractions in extended modular b-metric spaces with an application

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 alpha-nu-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.
Basque GovernmentBasque Government [IT1207-19]; Ege University Scientific Research Projects Coordination UnitEge University [FGA-2020-22080]
The authors would like to thank the editor and the anonymous referees for their careful reading of our manuscript and their many insightful comments and suggestions. The authors thank the Basque Government for its support of this work through Grant IT1207-19. This study is supported by Ege University Scientific Research Projects Coordination Unit. Project Number FGA-2020-22080.