Convergence Rate of Implicit Iteration Process and a Data Dependence Result

YILDIRIM İ., ABBAS M.

EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, cilt.11, sa.1, ss.189-201, 2018 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 11 Sayı: 1
  • Basım Tarihi: 2018
  • Dergi Adı: EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.189-201
  • Atatürk Üniversitesi Adresli: Evet

Özet

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.