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- W802400524 abstract "Abstract. In this paper, we consider the hybrid monotone projection al-gorithm for asymptotically quasi-pseudocontractive mappings. A strongconvergence theorem is established in the framework of Hilbert spaces.Our results mainly improve the corresponding results announced by [H.Zhou, Demiclosedness principle with applications for asymptotically pseudo-contractions in Hilbert spaces, Nonlinear Anal. 70 (2009) 3140-3145]and also include Kim and Xu [T.H. Kim, H.K. Xu, Strong convergenceof modi ed Mann iterations for asymptotically nonexpansive mappingsand semigroups, Nonlinear Anal. 64 (2006) 1140-1152; Convergence ofthe modi ed Mann’s iteration method for asymptotically strict pseudo-contractions, Nonlinear Anal. 68 (2008) 2828-2836] as special cases. 1. Introduction and PreliminariesThroughout this paper, we assume that His a real Hilbert space with innerproduct h;iand norm kk, respectively. Assume that Cis a nonempty closedconvex subset of Hand T: C!Cis a nonlinear mapping. We use F(T) todenote the set of xed points of T.Recall that the mapping T: C!Cis said to be nonexpansive ifkTx Tykkx yk; 8x;y2C: (1:1)The mapping T: C!Cis said to be asymptotically nonexpansive if thereexists a sequence fk" @default.
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- W802400524 date "2009-12-01" @default.
- W802400524 modified "2023-09-24" @default.
- W802400524 title "Hybrid monotone projection algorithms for asymptotically quasi-pseudocontractive mappings" @default.
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