## 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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