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  • Research Article
  • Open Access

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

Journal of Inequalities and Applications20102010:820535

  • Received: 31 October 2009
  • Accepted: 3 March 2010
  • Published:


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.


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

Publisher note

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Authors’ Affiliations

Division of Mathematical Sciences, Pukyong National University, Busan, 608-737, South Korea