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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:
47J25Iterative procedures (nonlinear operator equations)
47H20Semigroups of nonlinear operators
47H09Mappings defined by “shrinking” properties