An Iterative Algorithm to Approximate Fixed Points of Non-Linear Operators with an Application

Abstract

In this article, we study the JF iterative algorithm to approximate the fixed points of a non-linear operator that satisfies condition (E) in uniformly convex Banach spaces. Further, some weak and strong convergence results are presented for the same operator using the JF iterative algorithm. We also demonstrate that the JF iterative algorithm is weakly w2G-stable with respect to almost contractions. In connection with our results, we provide some illustrative numerical examples to show that the JF iterative algorithm converges faster than some well-known iterative algorithms. Finally, we apply the JF iterative algorithm to estimate the solution of a functional non-linear integral equation. The results of the present manuscript generalize and extend the results in existing literature and will draw the attention of researchers.