Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces. (English) Zbl 1134.47052

Takahashi, Wataru; Takeuchi, Yukio; Kubota, Rieko

J. Math. Anal. Appl. 341, No. 1, 276-286 (2008).

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.

Keywords:

nonexpansive mapping; fixed point; maximal monotone operator; one-parameter nonexpansive semigroup; hybrid method

Citations:

Zbl 1035.47048

References:

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