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Zbl 1156.47055
Kohsaka, Fumiaki; Takahashi, Wataru
Block iterative methods for a finite family of relatively nonexpansive mappings in Banach spaces. (English)
[J] Fixed Point Theory Appl. 2007, Article ID 21972, 18 p. (2007). ISSN 1687-1812/e

Summary: Using the convex combination based on Bregman distances due to {\it Y.\,Censor} and {\it S.\,Reich} [Optimization 37, No.\,4, 323--339 (1996; Zbl 0883.47063)], we define an operator from a given family of relatively nonexpansive mappings in a Banach space. We first prove that the fixed-point set of this operator is identical to the set of all common fixed points of the mappings. Next, using this operator, we construct an iterative sequence to approximate common fixed points of the family. We finally apply our results to a convex feasibility problem in Banach spaces.

MSC 2000:: *47J25 Methods for solving nonlinear operator equations (general)
47H09 Mappings defined by "shrinking" properties
47N10 Appl. of operator theory in optimization, math. programming, etc.

Citations: Zbl 0883.47063

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