Approximation of solutions for nonlinear functional integral equations

In this article, we consider a class of nonlinear functional integral equations, motivated by an equation that offers increasing evidence to the extant literature through replication studies. We investigate the existence of solution for nonlinear functional integral equations on Banach space C[0, 1]. We use the technique of the generalized Darbo's fixed-point theorem associated with the measure of noncompactness (MNC) to prove our existence result. Also, we have given two examples of the applicability of established existence result in the theory of functional integral equations. Further, we construct an efficient iterative algorithm to compute the solution of the first example, by employing the modified homotopy perturbation (MHP) method associated with Adomian decomposition. Moreover, the condition of convergence and an upper bound of errors are presented.

Automated summary

In this article, we investigate the existence of solutions for a class of nonlinear functional integral equations on the Banach space C[0, 1]. We use the technique of the generalized Darbo's fixed-point theorem associated with the measure of noncompactness (MNC) to prove our existence result. Additionally, we provide two examples of the applicability of the established existence result in the theory of functional integral equations. Furthermore, we construct an efficient iterative algorithm to compute the solution of one of the examples, using the modified homotopy perturbation (MHP) method associated with Adomian decomposition. We also present the convergence condition and an upper bound of errors.