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On the Solution of n‐Product of 2D‐Hadamard–Volterra Integral Equations in Banach Algebra

Author

Listed:
  • Mohamed M. A. Metwali
  • Manochehr Kazemi
  • Shami A. M. Alsallami

Abstract

In this study, the solvability of a general form of product type of n‐classes of 2D‐Hadamard–Volterra integral equations in the Banach algebra C([1, a] × [1, b]) is studied and investigated under more general and weaker assumptions. We use a general form of the Petryshyn’s fixed point theorem (F.P.T.) in combination with a suitable measure of noncompactness. This forms a generalization of the Schauder, Darbo, and classical Petryshyn’s F.P.T. The problem under study encompasses various integral equations, as different special cases have been previously investigated in the literature. Finally, we present several illustrative examples to validate our underlying assumptions.

Suggested Citation

  • Mohamed M. A. Metwali & Manochehr Kazemi & Shami A. M. Alsallami, 2025. "On the Solution of n‐Product of 2D‐Hadamard–Volterra Integral Equations in Banach Algebra," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:1132501
    DOI: 10.1155/jom/1132501
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    References listed on IDEAS

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    3. İsmet Özdemir & Ümit Çakan & Bekir İlhan, 2013. "On the Existence of the Solutions for Some Nonlinear Volterra Integral Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Sen, Mausumi & Saha, Dipankar & Agarwal, R.P., 2019. "A Darbo fixed point theory approach towards the existence of a functional integral equation in a Banach algebra," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 111-118.
    5. 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, John Wiley & Sons, vol. 2012(1).
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