1. Approximating solutions of variational inequalities for asymptotically nonexpansive mappings
- Author
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Chang, S.S., Lee, H.W.J., Chan, Chi Kin, and Kim, J.K.
- Subjects
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APPROXIMATION theory , *VARIATIONAL inequalities (Mathematics) , *NONEXPANSIVE mappings , *ASYMPTOTES , *BANACH spaces , *MATHEMATICAL sequences , *VISCOSITY solutions , *FIXED point theory - Abstract
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]. [Copyright &y& Elsevier]
- Published
- 2009
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