Convergence Rate of Implicit Iteration Process and a Data Dependence Result

Isa Yildirim, Mujahid Abbas

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.

Keywords

implicit iterations; convergence rate; data dependence.

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