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

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

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.

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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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Authors and Affiliations

  1. Departement of Mathematics, College of Education of Jubail, Dammam University, P.O: 12020, Industrial Jubail , 31961, Saudi Arabia

    Hassen Aydi & Manel Jellali

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

    Erdal Karapınar

Authors
  1. Hassen Aydi
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  2. Manel Jellali
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  3. Erdal Karapınar
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Correspondence to Hassen Aydi.

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Aydi, H., Jellali, M. & Karapınar, E. Common fixed points for generalized \(\alpha \)-implicit contractions in partial metric spaces: consequences and application. RACSAM 109, 367–384 (2015). https://doi.org/10.1007/s13398-014-0187-1

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  • DOI: https://doi.org/10.1007/s13398-014-0187-1

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