Convergence Rate of Implicit Iteration Process and a Data Dependence Result

Abstract

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 Ishikawatype 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.

Existence, error estimation, rate of convergence, Ulam-Hyers stability, well-posedness and limit shadowing property related to a fixed point problem

“…We also investigate the rate of convergence of the iteration process. Such considerations have appeared in the fixed point theory through works like [2,7,14,25].…”

An investigation of new quicker implicit iterations in hyperbolic spaces

“…Recently, Yildirim and Abbas [12] have introduced the following implicit S-iteration procedure and showed that the convergence rate of this iteration is higher than the iterations (2) and (1).…”