Krasnoselski-Mann Iterations for Hierarchical Fixed Point Problems for a Finite Family of Nonself Mappings in Banach Spaces |
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Authors: | L. C. Ceng A. Petruşel |
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Affiliation: | 1.Department of Mathematics,Shanghai Normal University,Shanghai,China;2.Department of Mathematics,Babe?-Bolyai University Cluj-Napoca,Cluj-Napoca,Romania |
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Abstract: | This paper deals with a method for approximating a solution of the following problem: find hierarchically a common fixed point of a finite family of nonself nonexpansive mappings with respect to a nonexpansive self mapping on a closed convex subset of a smooth and reflexive Banach space X, which admits a weakly sequentially continuous duality mapping. First, we prove a weak convergence theorem which extends and improves one recent result proved by Yao and Liou (see Inverse Problems 24 (2008), doi:). Secondly, when the self mapping is a contraction, we prove, under different restrictions on parameters, a strong convergence result which generalize some recent results in the literature. |
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