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Some New Generalization of Darbo’s Fixed Point Theorem and Its Application on Integral Equations

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  • Anupam Das

    (Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh 791112, Arunachal Pradesh, India
    These authors contributed equally to this work.)

  • Bipan Hazarika

    (Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh 791112, Arunachal Pradesh, India
    Department of Mathematics, Gauhati University, Guwahati 781014, Assam, India
    These authors contributed equally to this work.)

  • Poom Kumam

    (MUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
    These authors contributed equally to this work.)

Abstract

In this article, we propose some new fixed point theorem involving measure of noncompactness and control function. Further, we prove the existence of a solution of functional integral equations in two variables by using this fixed point theorem in Banach Algebra, and also illustrate the results with the help of an example.

Suggested Citation

  • Anupam Das & Bipan Hazarika & Poom Kumam, 2019. "Some New Generalization of Darbo’s Fixed Point Theorem and Its Application on Integral Equations," Mathematics, MDPI, vol. 7(3), pages 1-9, February.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:214-:d:209019
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    References listed on IDEAS

    as
    1. Dongxia Zan & Run Xu, 2018. "The Existence Results of Solutions for System of Fractional Differential Equations with Integral Boundary Conditions," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-8, October.
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