A modified halpern-type iteration algorithm for totally quasi-φ-asymptotically nonexpansive mappings with applications

S. S. Chang, Heung Wing Joseph Lee, Chi Kin Chan, W. B. Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

33 Citations (Scopus)


The purpose of this article is to modify the Halpern-type iteration algorithm for total quasi-φ-asymptotically nonexpansive mapping to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in the paper improve and extend the corresponding results of [X.L. Qin, Y.J. Cho, S.M. Kang, H. Y. Zhou, Convergence of a modified Halpern-type iterative algorithm for quasi-φ-nonexpansive mappings, Appl. Math. Lett. 22 (2009) 1051-1055], [Z.M. Wang, Y.F. Su, D.X. Wang, Y.C. Dong, A modified Halpern-type iteration algorithm for a family of hemi-relative nonexpansive mappings and systems of equilibrium problems in Banach spaces, J. Comput. Appl. Math. 235 (2011) 2364-2371], [Y.F. Su, H.K. Xu, X. Zhang, Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications, Nonlinear Anal. 73 (2010) 3890-3906], [C. Martinez-Yanes, H.K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006) 2400-2411] and others.
Original languageEnglish
Pages (from-to)6489-6497
Number of pages9
JournalApplied Mathematics and Computation
Issue number11
Publication statusPublished - 5 Feb 2012


  • Generalized projection
  • Halpern-type iteration algorithm
  • Nonexpansive mapping
  • Quasi-φ- nonexpansive mapping
  • Quasi-φ-symptotically nonexpansive mapping
  • Relatively nonexpansive mapping
  • Total quasi-φ-symptotically nonexpansive mapping
  • Weak relatively nonexpansive mapping

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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