A new hybrid method for solving a generalized equilibrium problem, solving a variational inequality problem and obtaining common fixed points in Banach spaces, with applications

Shih Sen Chang, Heung Wing Joseph Lee, Chi Kin Chan

Research output: Journal article publicationJournal articleAcademic researchpeer-review

55 Citations (Scopus)

Abstract

The purpose of this paper is to prove by using a new hybrid method a strong convergence theorem for finding a common element of the set of solutions for a generalized equilibrium problem, the set of solutions for a variational inequality problem and the set of common fixed points for a pair of relatively nonexpansive mappings in a Banach space. As applications, we utilize our results to obtain some new results for finding a solution of an equilibrium problem, a fixed point problem and a common zero-point problem for maximal monotone mappings in Banach spaces.
Original languageEnglish
Pages (from-to)2260-2270
Number of pages11
JournalNonlinear Analysis, Theory, Methods and Applications
Volume73
Issue number7
DOIs
Publication statusPublished - 1 Oct 2010

Keywords

  • α-inverse- strongly monotone mapping
  • Equilibrium problem
  • Generalized equilibrium problem
  • Maximal monotone operator
  • Relatively nonexpansive mapping
  • Variational inequality

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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