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<p>In this paper, we investigate a generalized nonlinear product type Fredholm–Volterra integral equation (G-NLPFVIE) and establish sufficient conditions ensuring the existence and uniqueness of its solution within the space <i>C</i>[<i>a</i>,&#xa0;<i>b</i>]. Next, we propose an algorithm based on the Adomian polynomial and the modified homotopy perturbation (mHPM) for approximating solutions to G-NLPFVIE. The convergence and error analysis of the proposed method are thoroughly discussed. Additionally, this work extends the findings of several previous studies. To validate the effectiveness of the proposed approach, illustrative examples are presented, demonstrating the application of mHPM in solving such equations.</p>

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Solvability and iterative algorithms for generalized nonlinear product type Fredholm–Volterra integral equations

  • 期刊论文

  • 发表日期：

    2025年9月8日

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  • Sukanta Halder,
  • Deepmala

摘要

In this paper, we investigate a generalized nonlinear product type Fredholm–Volterra integral equation (G-NLPFVIE) and establish sufficient conditions ensuring the existence and uniqueness of its solution within the space C[a, b]. Next, we propose an algorithm based on the Adomian polynomial and the modified homotopy perturbation (mHPM) for approximating solutions to G-NLPFVIE. The convergence and error analysis of the proposed method are thoroughly discussed. Additionally, this work extends the findings of several previous studies. To validate the effectiveness of the proposed approach, illustrative examples are presented, demonstrating the application of mHPM in solving such equations.