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Application of fixed point theorem to solvability of functional stochastic integral equations

Author

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  • Kazemi, M.
  • Yaghoobnia, A.R.

Abstract

In this paper, the existence of the solution of a class of nonlinear stochastic functional integral equations is investigated. Such that the concept of measures of noncompactness, and Petryshyn’s fixed point theorem in Banach space has been used. In addition to proving the theorems of the existence of the solution, by solving some examples, it is shown that the method is efficient. We also give an example that satisfies the conditions of our main theorem, while the conditions described in some other papers do not.

Suggested Citation

  • Kazemi, M. & Yaghoobnia, A.R., 2022. "Application of fixed point theorem to solvability of functional stochastic integral equations," Applied Mathematics and Computation, Elsevier, vol. 417(C).
    • Handle: RePEc:eee:apmaco:v:417:y:2022:i:c:s0096300321008419
    DOI: 10.1016/j.amc.2021.126759
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    References listed on IDEAS

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    1. 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).
    2. 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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    Cited by:

    1. Cao, Baiheng & Wu, Xuedong & Wang, Yaonan & Zhu, Zhiyu, 2024. "Modified hybrid B-spline estimation based on spatial regulator tensor network for burger equation with nonlinear fractional calculus," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 253-275.
    2. Diop, Amadou & Dieye, Moustapha & Hazarika, Bipan, 2022. "Random integrodifferential equations of Volterra type with delay : attractiveness and stability," Applied Mathematics and Computation, Elsevier, vol. 430(C).

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