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The Technique of Quadruple Fixed Points for Solving Functional Integral Equations under a Measure of Noncompactness

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  • Hasanen A. Hammad

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

  • Amal A. Khalil

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

Abstract

Under the idea of a measure of noncompactness, some fixed point results are proposed and a generalization of Darbo’s fixed point theorem is given in this manuscript. Furthermore, some novel quadruple fixed points results via a measure of noncompactness for a general class of functions are presented. Ultimately, the solutions to a system of non-linear functional integral equations by the fixed point results obtained are discussed, and non-trivial examples to illustrate the validity of our study are derived.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2130-:d:453137
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    References listed on IDEAS

    as
    1. Erdal Karapınar & Wasfi Shatanawi & Zead Mustafa, 2012. "Quadruple Fixed Point Theorems under Nonlinear Contractive Conditions in Partially Ordered Metric Spaces," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, July.
    2. Shatanawi, Wasfi, 2012. "Some fixed point results for a generalized ψ-weak contraction mappings in orbitally metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 520-526.
    3. 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.
    4. 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.
    5. Wasfi Shatanawi & Mihai Postolache, 2012. "Some Fixed-Point Results for a -Weak Contraction in -Metric Spaces," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-19, October.
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