Hybrid iterative method for finding common solutions of generalized mixed equilibrium and fixed point problems

Lu Chuan Ceng, Sy Ming Guu*, Jen Chih Yao

*Corresponding author for this work

Research output: Contribution to journalJournal Article peer-review

39 Scopus citations

Abstract

Recently, Colao et al. (J Math Anal Appl 344:340-352, 2008) introduced a hybrid viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a finite family of nonexpansive mappings in a real Hilbert space. In this paper, by combining Colao, Marino and Xu's hybrid viscosity approximation method and Yamada's hybrid steepest-descent method, we propose a hybrid iterative method for finding a common element of the set GMEP of solutions of a generalized mixed equilibrium problem and the set ∩Ni=1 Fix (S i) of fixed points of a finite family of nonexpansive mappings {Si}Ni = 1 in a real Hilbert space. We prove the strong convergence of the proposed iterative algorithm to an element of ∩Ni=1 Fix (Si) ∩ GMEP, which is the unique solution of a variational inequality.

Original languageEnglish
Article number92
JournalFixed Point Theory and Applications
Volume2012
DOIs
StatePublished - 2012
Externally publishedYes

Keywords

  • Fixed point
  • Generalized mixed equilibrium problem
  • Hybrid iterative method
  • Nonexpansive mapping
  • Variational inequality

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