Krasnoselski-Mann Iterations for Hierarchical Fixed Point Problems for a Finite Family of Nonself Mappings in Banach Spaces

L. C. Ceng () and A. Petruşel ()
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L. C. Ceng: Shanghai Normal University
A. Petruşel: Babeş-Bolyai University Cluj-Napoca

Journal of Optimization Theory and Applications, 2010, vol. 146, issue 3, No 5, 617-639

Abstract: 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: 10.1088/0266-5611/24/1/015015 ). 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.

Keywords: Modified Krasnoselski-Mann iteration; Hierarchical fixed point problem; Nonexpansive mapping; Weak convergence; Strong convergence; Reflexive Banach space; Demiclosedness; Contraction mapping (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10957-010-9679-0

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