The Meir-Keeler type contractions in extended modular $ b $-metric spaces with an application
Articles > Article · 2020
Authors: Abdolsattar Gholidahneh, Shaban Sedghi, Özgür EGE, Zoran D. Mitrovic, Manuel De La Sen
AIMS Mathematics, Journal Indexed in SCI Expanded, International, WoS, 2020, vol 6, pp 1781-1799
DOI: 10.3934/math.2021107
Summary
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 $-$ \widehat{\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.