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Fixed point theorems in new generalized metric spaces

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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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Authors and Affiliations

  1. Department of Mathematics, Atilim University, 06836, İncek, Ankara, Turkey

    Erdal Karapınar

  2. Nonlinear Analysis and Applied Mathematics Research Group (NAAM), King Abdulaziz University, Jeddah, Saudi Arabia

    Erdal Karapınar

  3. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

    Donal O’Regan

  4. Department of Quantitative Methods for Economics and Business, University of Granada, Granada, Spain

    Antonio Francisco Roldán López de Hierro

  5. PAIDI Research Group FQM-268, University of Jaén, Jaén, Spain

    Antonio Francisco Roldán López de Hierro

  6. Operator Theory and Applications Research Group, Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Naseer Shahzad

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  1. Erdal Karapınar
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  2. Donal O’Regan
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  3. Antonio Francisco Roldán López de Hierro
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  4. Naseer Shahzad
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Correspondence to Antonio Francisco Roldán López de Hierro.

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Karapınar, E., O’Regan, D., Roldán López de Hierro, A.F. et al. Fixed point theorems in new generalized metric spaces. J. Fixed Point Theory Appl. 18, 645–671 (2016). https://doi.org/10.1007/s11784-016-0301-4

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  • DOI: https://doi.org/10.1007/s11784-016-0301-4

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