Fixed point theorems in new generalized metric spaces |
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| Authors: | Erdal Karapınar Donal O’Regan Antonio Francisco Roldán López de Hierro Naseer Shahzad |
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| Affiliation: | 1.Department of Mathematics,Atilim University,?ncek, Ankara,Turkey;2.Nonlinear Analysis and Applied Mathematics Research Group (NAAM),King Abdulaziz University,Jeddah,Saudi Arabia;3.School of Mathematics, Statistics and Applied Mathematics,National University of Ireland,Galway,Ireland;4.Department of Quantitative Methods for Economics and Business,University of Granada,Granada,Spain;5.PAIDI Research Group FQM-268,University of Jaén,Jaén,Spain;6.Operator Theory and Applications Research Group, Department of Mathematics,King Abdulaziz University,Jeddah,Saudi Arabia |
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| Abstract: | The aim of our paper is to present new fixed point theorems under very general contractive conditions in generalized metric spaces which were recently introduced by Jleli and Samet in [Fixed Point Theory Appl. 2015 (2015), doi: 10.1186/s13663-015-0312-7]. Although these spaces are not endowed with a triangle inequality, these spaces extend some well known abstract metric spaces (for example, b-metric spaces, Hitzler–Seda metric spaces, modular spaces with the Fatou property, etc.). We handle several types of contractive conditions. The main theorems we present involve a reflexive and transitive binary relation that is not necessarily a partial order. We give a counterexample to a recent fixed point result of Jleli and Samet. Our results extend and unify recent results in the context of partially ordered abstract metric spaces. |
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