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Common fixed points for generalized \(\alpha \)-implicit contractions in partial metric spaces: consequences and application

  • Hassen AydiEmail author
  • Manel Jellali
  • Erdal Karapınar
Original Paper

Abstract

In this paper, we introduce the concept of generalized \(\alpha \)-admissible pair of mappings generalizing the definition of \(\alpha \)-admissible mappings presented by Samet et al. (Nonlinear Anal 75:2154–2165, 2012). Based on above, we define generalized \(\alpha \)-implicit contractions in the setting of partial metric spaces and we provide some common fixed point results for such contractions. We also derive some consequences and corollaries from our obtained results. An application and some examples are presented making effective the new concepts and results.

Keywords

Common fixed point Implicit contraction Partial metric space 

Mathematics Subject Classification

47H10 54H25 46J10 

Notes

Acknowledgments

The authors express their gratitude to the referees for constructive and useful remarks and suggestions. The authors gratefully also acknowledge the support from the Deanship of Scientific Research (DSR) at Dammam University during this research.

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Copyright information

© Springer-Verlag Italia 2014

Authors and Affiliations

  1. 1.Departement of Mathematics, College of Education of JubailDammam UniversityIndustrial Jubail Saudi Arabia
  2. 2.Department of MathematicsAtilim UniversityAnkaraTurkey

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