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Approximating fixed points of infinite nonexpansive mappings by the hybrid method. (English) Zbl 1033.65037

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.

MSC:

65J15 Numerical solutions to equations with nonlinear operators
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems
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References:

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