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Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces. (English) Zbl 1134.47052
Summary: We prove a strong convergence theorem by the hybrid method for a family of nonexpansive mappings which generalizes the theorems of K. Nakajo and W. Takahashi [J. Math. Anal. Appl. 279, No. 2, 372–379 (2003; Zbl 1035.47048)]. Furthermore, we obtain another strong convergence theorem for the family of nonexpansive mappings by a hybrid method which is different from the one of Nakajo and Takahashi. Using this theorem, we get some new results for a single nonexpansive mapping or a family of nonexpansive mappings in a Hilbert space.

MSC:
47J25 Iterative procedures involving nonlinear operators
47H20 Semigroups of nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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