Strong convergence result for Meir-Keeler contractions and a countable family of accretive operators in Banach spaces with applications

Abstract

In this paper we introduce an iterative algorithm with Meir-Keeler contractions for finding zeros of the sum of finite families of $m$-accretive operators and finite family of $\alpha$-inverse strongly accretive operators in a real smooth and uniformly convex Banach spaces. We also discuss application of this method to the approximation of solution to certain integro-differential equation with generalized $p$-Laplacian operators. Our results improves and compliments many recent and important results in the literature.