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Strong convergence theorems for a finite family of nonexpansive mappings and applications. (English) Zbl 1055.47514

Summary: We first consider an iteration scheme given by a finite family of nonexpansive mappings and then prove a strong convergence theorem for a finite family of nonexpansive mappings in a Banach space. Further, using the result, we prove a strong convergence theorem which is connected with the problem of image recovery. Finally, we consider the problem of finding a common fixed point for a finite commuting family of nonexpansive mappings in a Banach space.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
49M05 Numerical methods based on necessary conditions
47N60 Applications of operator theory in chemistry and life sciences
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