Skip to main content

Advertisement

Implicit Iteration Methods with Errors for Discrete Non-Lipschitzian Families with Perturbed Mappings

Article metrics

  • 869 Accesses

Abstract

Motivated and inspired by the recent works on implicit iteration methods, we prove necessary and sufficient conditions for strong convergence of the eventually implicit iteration methods with errors to a common fixed point of a discrete family which is continuous total asymptotically nonexpansive (in brief, TAN) on -uniformly smooth Banach spaces with a perturbed mapping , , under some suitable control conditions of parameters. Some applications to viscosity approximation methods or to the eventually implicit algorithms with errors for a finite family of TAN self-mappings in real Banach spaces are also added.

Publisher note

To access the full article, please see PDF.

Author information

Correspondence to Tae-Hwa Kim.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Kim, T., Kim, K. Implicit Iteration Methods with Errors for Discrete Non-Lipschitzian Families with Perturbed Mappings. J Inequal Appl 2010, 820535 (2010) doi:10.1155/2010/820535

Download citation

Keywords

  • Iteration Method
  • Full Article
  • Publisher Note
  • Implicit Iteration
  • Perturbed Mapping