Convergence rate of implicit iteration process and a data dependence result

Abstract

The aim of this paper is to introduce an implicit S-iteration process and study its convergence in the framework of W-hyperbolic spaces. We show that the implicit S-iteration process has higher rate of convergence than implicit Mann type iteration and implicit Ishikawa-type iteration processes. We present a numerical example to support the analytic result proved herein. Finally, we prove a data dependence result for a contractive type mapping using implicit S-iteration process.