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Zbl 1033.65037
Kikkawa, M.; Takahashi, W.
Approximating fixed points of infinite nonexpansive mappings by the hybrid method. (English)
[J] J. Optimization Theory Appl. 117, No. 1, 93-101 (2003). ISSN 0022-3239; ISSN 1573-2878/e

The authors, first, introduce an iterative scheme for finding a common point of infinite nonexpansive mappings $T_i$, $i=1, 2, \ldots$ in a Hilbert space $H$ by using a hybrid method, where $T_i$ is a nonexpansive mapping of $C$ into itself and $C\subset H$ is a nonempty closed convex set. Next, they prove a strong convergence theorem which is connected with the problem of image recovery. Furthermore, using the above result, they consider a generalized problem of image recovery and the problem of finding a common fixed point of a family of nonexpansive mappings.
[Yu Wenhuan (Tianjin)]

MSC 2000:: *65J15 Equations with nonlinear operators (numerical methods)
94A08 Image processing
47H09 Mappings defined by "shrinking" properties
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: nonexpansive mapping; hybrid method; fixed point; image recovery; Hilbert space; convergence

Cited in: Zbl 1199.47297 Zbl 1140.47057

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