Approximating solutions of variational inequalities for asymptotically nonexpansive mappings

S. S. Chang, Heung Wing Joseph Lee, Chi Kin Chan, J. K. Kim

Research output: Journal article publicationJournal articleAcademic researchpeer-review

14 Citations (Scopus)

Abstract

By using viscosity approximation methods for asymptotically nonexpansive mappings in Banach spaces, some sufficient and necessary conditions for a new type of iterative sequences to converging to a fixed point which is also the unique solution of some variational inequalities are obtained. The results presented in the paper extend and improve some recent results in [C.E. Chidume, Jinlu Li, A. Udomene, Convergence of paths and approximation of fixed points of asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 138 (2) (2005) 473-480; N. Shahzad, A. Udomene, Fixed point solutions of variational inequalities for asymptotically nonexpansive mappings in Banach spaces, Nonlinear Anal. 64 (2006) 558-567; T.C. Lim, H.K. Xu, Fixed point theories for asymptotically nonexpansive mappings, Nonlinear Anal. TMA, 22 (1994) 1345-1355; H.K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl., 298 (2004) 279-291].
Original languageEnglish
Pages (from-to)51-59
Number of pages9
JournalApplied Mathematics and Computation
Volume212
Issue number1
DOIs
Publication statusPublished - 1 Jun 2009

Keywords

  • Asymptotically nonexpansive mappings
  • Fixed point
  • Normalized duality mapping
  • Uniform normal structure
  • Uniformly Gâteaux differentiable norm
  • Viscosity approximation

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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