On a hybrid method for a family of relatively nonexpansive mappings in a Banach space

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:357

Article

Kimura, Yasunori¹  Takahashi, Wataru¹ 

[1] Tokyo Inst Technol, Dept Math & Comp Sci, Tokyo 1528552, Japan

关键词: Nonexpansive mapping;    Relatively nonexpansive mapping;    Hybrid method;    Approximation;    Fixed point;    Maximal monotone operator;    Resolvent;    Metric projection;    Generalized projection;   

DOI  :  10.1016/j.jmaa.2009.03.052

来源: Elsevier

【 摘 要 】

We prove strong convergence theorems by the hybrid method given by Takahashi, Takeuchi, and Kubota for a family of relatively nonexpansive mappings under weaker conditions. The method of the proof is different from the original one and it shows that the type of projection used in the iterative method is independent of the properties of the mappings. We also deal with the problem of finding a zero of a maximal monotone operator and obtain a strong convergence theorem using this method. (C) 2009 Elsevier Inc. All rights reserved.

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