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Common Fixed Point and Coupled Coincidence Point Theorems for Geraghty’s Type Contraction Mapping with Two Metrics Endowed with a Directed Graph

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  • P. Charoensawan
  • W. Atiponrat

Abstract

The purpose of this paper is to present some existence and uniqueness results for common fixed point theorems for - contraction mappings with two metrics endowed with a directed graph. In addition, by using our main results, we obtain some results about coupled coincidence points endowed with a directed graph. Our results generalize those presented in previous papers.

Suggested Citation

  • P. Charoensawan & W. Atiponrat, 2017. "Common Fixed Point and Coupled Coincidence Point Theorems for Geraghty’s Type Contraction Mapping with Two Metrics Endowed with a Directed Graph," Journal of Mathematics, Hindawi, vol. 2017, pages 1-9, November.
    • Handle: RePEc:hin:jjmath:5746704
    DOI: 10.1155/2017/5746704
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    References listed on IDEAS

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    1. M. R. Alfuraidan & M. A. Khamsi, 2014. "Caristi Fixed Point Theorem in Metric Spaces with a Graph," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-5, March.
    2. Gerald Jungck, 1986. "Compatible mappings and common fixed points," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 9, pages 1-9, January.
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    Cited by:

    1. Watchareepan Atiponrat & Pariwate Varnakovida & Pharunyou Chanthorn & Teeranush Suebcharoen & Phakdi Charoensawan, 2023. "Common Fixed Point Theorems for Novel Admissible Contraction with Applications in Fractional and Ordinary Differential Equations," Mathematics, MDPI, vol. 11(15), pages 1-20, August.
    2. Reny George & Ekta Tamrakar & Jelena Vujaković & Hemant Kumar Pathak & Selvavinayagam Velusamy, 2019. "( C , Ψ * , G ) Class of Contractions and Fixed Points in a Metric Space Endowed with a Graph," Mathematics, MDPI, vol. 7(5), pages 1-19, May.

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