Convergence and Data Dependency of Normal-S Iterative Method for Discontinuous Operators on Banach Space


Gursoy F., KHAN A. R. , Erturk M., KARAKAYA V.

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, vol.39, no.3, pp.322-345, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 39 Issue: 3
  • Publication Date: 2018
  • Doi Number: 10.1080/01630563.2017.1363774
  • Journal Name: NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.322-345
  • Keywords: Collage theorem, data dependency, inverse problem, iterative scheme, strong convergence, COLLAGE-BASED APPROACH, INVERSE PROBLEMS, FIXED-POINTS, APPROXIMATION, EQUATIONS, MAPPINGS, MAPS

Abstract

We study convergence, rate of convergence and data dependency of normal-S iterative method for a fixed point of a discontinuous operator T on a Banach space. We also prove some Collage type theorems for T. The main aim here is to show that there is a close relationship between the concepts of data dependency of fixed points and the collage theorems and show that the latter provides better estimate. Numerical examples in support of the results obtained are also given.