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Zbl 1166.47058
Kimura, Yasunori; Takahashi, Wataru
On a hybrid method for a family of relatively nonexpansive mappings in a Banach space. (English)
[J] J. Math. Anal. Appl. 357, No. 2, 356-363 (2009). ISSN 0022-247X

Summary: We prove strong convergence theorems by the hybrid method given by {\it W.\,Takahashi, Y.\,Takeuchi} and {\it R.\,Kubota} [J.~Math.\ Anal.\ Appl.\ 341, No.\,1, 276--286 (2008; Zbl 1134.47052)] 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.

MSC 2000:: *47J25 Methods for solving nonlinear operator equations (general)
47H09 Mappings defined by "shrinking" properties
47H05 Monotone operators (with respect to duality)

Keywords: nonexpansive mapping; relatively nonexpansive mapping; hybrid method; approximation; fixed point; maximal monotone operator; resolvent; metric projection; generalized projection

Citations: Zbl 1134.47052

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