%0 Journal Article %T An Application of Fixed Point Theory to A Nonlinear Integral Equation in Banach Spaces %J Communications in Nonlinear Analysis %I Research & Science Group Ltd. %Z 2371-7920 %A Ofem, Austine Efut %D 2023 %\ 03/01/2023 %V 11 %N 1 %P 1-16 %! An Application of Fixed Point Theory to A Nonlinear Integral Equation in Banach Spaces %K fixed point %K Banach space %K Strong convergence %K nonlinear integral equation %K data dependence %R %X 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 \cite{Berin} that our new iterative scheme 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 to 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. %U https://www.cna-journal.com/article_112710_4a498a48f6aa3f7ed071cced98bc1228.pdf