Modified block iterative algorithm for Quasi-φ-asymptotically nonexpansive mappings and equilibrium problem in banach spaces

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

Research output: Journal article publicationJournal articleAcademic researchpeer-review

46 Citations (Scopus)


The purpose of this paper is to propose a modified block iterative algorithm for find a common element of the set of common fixed points of an infinite family of quasi-φ-asymptotically nonexpansive mappings and the set of an equilibrium problem. Under suitable conditions, some strong convergence theorems are established in a uniformly smooth and strictly convex Banach space with the Kadec-Klee property. As an application, at the end of the paper a numerical example is given. The results presented in the paper improve and extend the corresponding results in Qin et al. [Convergence theorems of common elements for equilibrium problems and fixed point problem in Banach spaces, J. Comput. Appl. Math., 225, 2009, 20-30], Zhou et al. [Convergence theorems of a modified hybrid algorithm for a family of quasi-φ-asymptotically nonexpansive mappings, J. Appl. Math. Compt., 17 March, 2009, doi:10.1007/s12190-009-0263-4], Takahashi and Zembayshi [Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces, Nonlinear Anal., 70, 2009, 45-57], Wattanawitoon and Kumam [Strong convergence theorems by a new hybrid projection algorithm for fixed point problem and equilibrium problems of two relatively quasi-nonexpansive mappings, Nonlinear Anal. Hybrid Syst., 3, 2009, 11-20] and Matsushita and Takahashi [A strong convergence theorem for relatively nonexpansive mappings in Banach spaces, J. Approx. Theory, 134, 2005, 257-266] and others.
Original languageEnglish
Pages (from-to)7520-7530
Number of pages11
JournalApplied Mathematics and Computation
Issue number18
Publication statusPublished - 15 May 2011


  • Equilibrium problem
  • Generalized projection
  • Modified block iterative algorithm
  • Quasi-φ-asymptotically nonexpansive mapping
  • Quasi-φ-nonexpansive mapping
  • Relatively nonexpansive mapping

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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