Solution of a Nonlinear Integral Equation via New Fixed Point Iteration Process

TL;DR

This paper presents a new three-step fixed point iteration method in Banach spaces that converges faster than existing methods and applies it to solve nonlinear integral equations.

Contribution

Introduction of a novel three-step iteration process with proven faster convergence for fixed points and application to nonlinear integral equations.

Findings

The new iteration converges faster than existing methods.

Proven convergence for fixed points of nonexpansive mappings.

Application to solve mixed type Volterra-Fredholm nonlinear integral equations.

Abstract

In this paper, we introduce a new three-step iteration process in Banach space and prove convergence results for approximating fixed points for nonexpansive mappings. Also, we show that the newly introduced iteration process converges faster than a number of existing iteration processes. Further, we discuss about the solution of mixed type Volterra-Fredholm functional nonlinear integral equation.