AN APPLICATION OF FIXED POINT THEORY TO A NONLINEAR INTEGRAL EQUATION IN BANACH SPACE

Document Type: Original Article

Author

Department of Mathematics, University of Uyo, Uyo, Nigeria.

Abstract

In this paper we propose a new iterative scheme, called the AF iteration process, for approximating the unique solution of a mixed type Volterra-
Fredholm functional nonlinear integral equation. We prove in the sense of Berinde [8] that our new iterative converges at a rate faster than some of the leading iterative schemes in the literature which have been employed recently to approximate the unique solution of a mixed type Volterra Fredholm functional nonlinear integral equation. We also prove that our new iterative method converges strongly the unique solution of a mixed type Volterra Fredholm functional nonlinear integral equation. In addition, we give data dependence result for the solution of the nonlinear integral equation which we are considering with the help of our new iterative scheme. Our results improve and unify some well known results in the existing literature.

Keywords


Articles in Press, Accepted Manuscript
Available Online from 11 August 2020