TY - JOUR ID - 112710 TI - An Application of Fixed Point Theory to A Nonlinear Integral Equation in Banach Spaces JO - Communications in Nonlinear Analysis JA - CNA LA - en SN - AU - Ofem, Austine Efut AD - Department of Mathematics, University of Uyo, Uyo, Nigeria. Y1 - 2023 PY - 2023 VL - 11 IS - 1 SP - 1 EP - 16 KW - fixed point KW - Banach space KW - Strong convergence KW - nonlinear integral equation KW - data dependence DO - N2 - 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. UR - https://www.cna-journal.com/article_112710.html L1 - https://www.cna-journal.com/article_112710_4a498a48f6aa3f7ed071cced98bc1228.pdf ER -