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Solvability of nonlinear quadratic integral equation by using simulation type condensing operator and measure of noncompactness

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  • Rabbani, Mohsen
  • Arab, Reza
  • Hazarika, Bipan

Abstract

The aim of this article is to prove the existence of solution for nonlinear quadratic integral equations using the generalized form of Darbo fixed point theorem with the help of measure of noncompactness and simulation type condensing operator in the Banach space L2[0, 1]. To illustrate validity of the analytical results, we present a nonlinear integral equation as an application. Finally, we introduce an iteration algorithm by modified homotopy perturbation and Adomian decomposition method to find solution of the above problem with a high accuracy.

Suggested Citation

  • Rabbani, Mohsen & Arab, Reza & Hazarika, Bipan, 2019. "Solvability of nonlinear quadratic integral equation by using simulation type condensing operator and measure of noncompactness," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 102-117.
    • Handle: RePEc:eee:apmaco:v:349:y:2019:i:c:p:102-117
    DOI: 10.1016/j.amc.2018.12.033
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    References listed on IDEAS

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    1. Khosravi, Hassan & Allahyari, Reza & Haghighi, Ali Shole, 2015. "Existence of solutions of functional integral equations of convolution type using a new construction of a measure of noncompactness on Lp(R+)," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 140-147.
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    Cited by:

    1. Rabbani, Mohsen & Das, Anupam & Hazarika, Bipan & Arab, Reza, 2020. "Measure of noncompactness of a new space of tempered sequences and its application on fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    2. Deep, Amar & Deepmala, & Ezzati, R., 2021. "Application of Petryshyn’s fixed point theorem to solvability for functional integral equations," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    3. Deep, Amar & Deepmala, & Rabbani, Mohsen, 2021. "A numerical method for solvability of some non-linear functional integral equations," Applied Mathematics and Computation, Elsevier, vol. 402(C).

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