Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces |
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| Authors: | Wataru Takahashi Yukio Takeuchi |
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| Institution: | a Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8552, Japan
b Division of Physics, Electrical and Computer Engineering, Graduate School of Engineering, Yokohama National University, Yokohama 240-8501, Japan |
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| Abstract: | In this paper, we prove a strong convergence theorem by the hybrid method for a family of nonexpansive mappings which generalizes Nakajo and Takahashi's theorems K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372-379], simultaneously. Furthermore, we obtain another strong convergence theorem for the family of nonexpansive mappings by a hybrid method which is different from 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. |
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| Keywords: | Nonexpansive mapping Fixed point Maximal monotone operator One-parameter nonexpansive semigroup Hybrid method |
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