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( C , Ψ * , G ) Class of Contractions and Fixed Points in a Metric Space Endowed with a Graph

Author

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  • Reny George

    (Department of Mathematics, College of Science, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
    Department of Mathematics and Computer Science, St. Thomas College, Bhilai, Chhattisgarh 490006, India)

  • Ekta Tamrakar

    (School of Studies in Mathematics, Pt. Ravishankar Shukla University, Raipur (C.G.) 492010, India)

  • Jelena Vujaković

    (Faculty of Sciences and Mathematics, University of Privstina, Kosovska Mitrovica 38220, Serbia)

  • Hemant Kumar Pathak

    (School of Studies in Mathematics, Pt. Ravishankar Shukla University, Raipur (C.G.) 492010, India)

  • Selvavinayagam Velusamy

    (Nasser Vocational Training Centre, Jau, Kingdom of Bahrain)

Abstract

In this paper, we introduce the ( C , Ψ * , G ) class of contraction mappings using C -class functions and some improved control functions for a pair of set valued mappings as well as a pair of single-valued mappings, and prove common fixed point theorems for such mappings in a metric space endowed with a graph. Our results unify and generalize many important fixed point results existing in literature. As an application of our main result, we have derived fixed point theorems for a pair of α -admissible set valued mappings in a metric space.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:482-:d:234738
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    References listed on IDEAS

    as
    1. 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.
    2. Hassen Aydi & Erdal Karapınar & Bessem Samet, 2012. "Fixed Point Theorems for Various Classes of Cyclic Mappings," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-15, October.
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