Convergence Rate of Implicit Iteration Process and a Data Dependence Result

Authors

  • Isa Yildirim Department of Mathematics, Faculty of Sceience, Ataturk University, 25240 Erzurum, Turkey
  • Mujahid Abbas

DOI:

https://doi.org/10.29020/nybg.ejpam.v11i1.2911

Keywords:

implicit iterations, convergence rate, data dependence.

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.

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Published

2018-01-30

Issue

Section

Wave Theory

How to Cite

Convergence Rate of Implicit Iteration Process and a Data Dependence Result. (2018). European Journal of Pure and Applied Mathematics, 11(1), 189-201. https://doi.org/10.29020/nybg.ejpam.v11i1.2911