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A Coupled Fixed Point Technique for Solving Coupled Systems of Functional and Nonlinear Integral Equations

Author

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  • Hasanen Abuelmagd Hammad

    (Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt)

  • Manuel De la Sen

    (Institute of Research and Development of Processes University of the Basque Country, 48940 Leioa, Spain)

Abstract

In this paper, we obtain coupled fixed point results for F -contraction mapping satisfying a nonlinear contraction condition in the framework of complete metric space without and with a directed graph. As applications of our results, we study a problem of existence and uniqueness of solutions for a class of systems of functional equations that appears in dynamic programming and nonlinear integral equations. Finally, illustrative examples to support some our results are discussed.

Suggested Citation

  • Hasanen Abuelmagd Hammad & Manuel De la Sen, 2019. "A Coupled Fixed Point Technique for Solving Coupled Systems of Functional and Nonlinear Integral Equations," Mathematics, MDPI, vol. 7(7), pages 1-18, July.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:634-:d:249243
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    References listed on IDEAS

    as
    1. Ravi P. Agarwal & Nawab Hussain & Mohamed-Aziz Taoudi, 2012. "Fixed Point Theorems in Ordered Banach Spaces and Applications to Nonlinear Integral Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, July.
    2. Hassen Aydi, 2011. "Some Coupled Fixed Point Results on Partial Metric Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-11, May.
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    Cited by:

    1. Hasanen A. Hammad & Manuel De la Sen, 2021. "Exciting Fixed Point Results under a New Control Function with Supportive Application in Fuzzy Cone Metric Spaces," Mathematics, MDPI, vol. 9(18), pages 1-23, September.
    2. Hasanen A. Hammad & Manuel De la Sen, 2020. "Fixed-Point Results for a Generalized Almost ( s , q )—Jaggi F -Contraction-Type on b —Metric-Like Spaces," Mathematics, MDPI, vol. 8(1), pages 1-21, January.
    3. Hasanen A. Hammad & Amal A. Khalil, 2020. "The Technique of Quadruple Fixed Points for Solving Functional Integral Equations under a Measure of Noncompactness," Mathematics, MDPI, vol. 8(12), pages 1-21, November.

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