Journal of Fixed Point Theory and Applications

, Volume 18, Issue 3, pp 645–671 | Cite as

Fixed point theorems in new generalized metric spaces

  • Erdal Karapınar
  • Donal O’Regan
  • Antonio Francisco Roldán López de Hierro
  • Naseer Shahzad


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.


Generalized metric space b-metric space fixed point contractive mapping 

Mathematics Subject Classification

Primary 47H10 46T99 Secondary 47H09 54H25 


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • Erdal Karapınar
    • 1
    • 2
  • Donal O’Regan
    • 3
  • Antonio Francisco Roldán López de Hierro
    • 4
    • 5
  • Naseer Shahzad
    • 6
  1. 1.Department of MathematicsAtilim Universityİncek, AnkaraTurkey
  2. 2.Nonlinear Analysis and Applied Mathematics Research Group (NAAM)King Abdulaziz UniversityJeddahSaudi Arabia
  3. 3.School of Mathematics, Statistics and Applied MathematicsNational University of IrelandGalwayIreland
  4. 4.Department of Quantitative Methods for Economics and BusinessUniversity of GranadaGranadaSpain
  5. 5.PAIDI Research Group FQM-268University of JaénJaénSpain
  6. 6.Operator Theory and Applications Research Group, Department of MathematicsKing Abdulaziz UniversityJeddahSaudi Arabia

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