Convergence Rate of Implicit Iteration Process and a Data Dependence Result

YILDIRIM İ., ABBAS M.

EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, vol.11, no.1, pp.189-201, 2018 (ESCI, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 1
  • Publication Date: 2018
  • Journal Name: EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.189-201
  • Ataturk University Affiliated: Yes

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.