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  • Research Article
  • Open Access

Weak and Strong Convergence Theorems of an Implicit Iteration Process for a Countable Family of Nonexpansive Mappings

  • 1,
  • 2 and
  • 1Email author
Fixed Point Theory and Applications20082008:732193

https://doi.org/10.1155/2008/732193

  • Received: 22 July 2008
  • Accepted: 18 November 2008
  • Published:

Abstract

Using the implicit iteration and the hybrid method in mathematical programming, we prove weak and strong convergence theorems for finding common fixed points of a countable family of nonexpansive mappings in a real Hilbert space. Our results include many convergence theorems by Xu and Ori (2001) and Zhang and Su (2007) as special cases. We also apply our method to find a common element to the set of fixed points of a nonexpansive mapping and the set of solutions of an equilibrium problem. Finally, we propose an iteration to obtain convergence theorems for a continuous monotone mapping.

Keywords

  • Hilbert Space
  • Mathematical Programming
  • Differential Geometry
  • Convergence Theorem
  • Hybrid Method

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Authors’ Affiliations

(1)
Department of Mathematics, Khon Kaen University, Khon Kaen, 40002, Thailand
(2)
Department of Mathematics, Statistics and Computer, Ubon Rajathanee University, Ubon Ratchathani, 34190, Thailand

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