Strong convergence theorems by hybrid methods for families of relatively nonexpansive mappings in Hilbert spaces

In 2008, Takahashi, Takeuchi and Kubota [10] proved a strong convergence theorem by the hybrid method for a family of nonexpansive mappings which generalized Nakajo and Takahashi's theorems [6]. Furthermore, they obtained another strong convergence theorem for the family of nonexpansive mapping...

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Bibliographic Details
Main Authors: T. Butsan, S. Dhompongsa, W. Takahashi
Format: Journal
Published: 2018
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Online Access:https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84894051431&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/50986
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Institution: Chiang Mai University
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Summary:In 2008, Takahashi, Takeuchi and Kubota [10] proved a strong convergence theorem by the hybrid method for a family of nonexpansive mappings which generalized Nakajo and Takahashi's theorems [6]. Furthermore, they obtained another strong convergence theorem for the family of nonexpansive mappings by a hybrid method which is different from Nakajo and Takahashi. In this paper, we extend Takahashi, Takeuchi and Kubota's results for a single relatively nonexpansive mapping or a family of relatively nonexpansive mappings in a Hilbert space. Using these results, we obtain some new strong convergence theorems in a Hilbert space. © 2010 yokohama publishers.