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

Vol. 11 No. 1: (January 2018)

License

Upon acceptance of an article by the journal, the author(s) accept(s) the transfer of copyright of the article to European Journal of Pure and Applied Mathematics.

European Journal of Pure and Applied Mathematics will be Copyright Holder.

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