Approximation of the fixed point of the product of two operators in Banach algebras with applications to some functional equations

TL;DR

This paper investigates the existence, uniqueness, and approximation of fixed points for the product of two nonlinear operators in Banach algebras, with applications to functional equations and numerical examples.

Contribution

It introduces a new approximation method for fixed points of hybrid nonlinear equations in Banach algebras and demonstrates its application to different functional equations.

Findings

Established existence and uniqueness of fixed points for operator products

Developed an approximation method for fixed points in Banach algebras

Provided numerical examples illustrating the method's applicability

Abstract

In this paper, the existence and uniqueness of the fixed point for the product of two nonlinear operator in Banach algebra is discussed. In addition, an approximation method of the fixed point of hybrid nonlinear equations in Banach algebras is established. This method is applied to two interesting different types of functional equations. In addition, to illustrate the applicability of our results we give some numerical examples.