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Strong convergence theorems by the hybrid method for families of mappings in Banach spaces

Let C be a nonempty closed convex subset of a uniformly convex Banach space E whose norm is Gâteaux differentiable and let { T n } be a family of mappings of C into itself such that the set of all common fixed points of { T n } is nonempty. We consider a sequence { x n } generated by the hybrid meth...

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Bibliographic Details
Published in:Nonlinear analysis 2009-08, Vol.71 (3), p.812-818
Main Authors: Nakajo, Kazuhide, Shimoji, Kazuya, Takahashi, Wataru
Format: Article
Language:English
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Summary:Let C be a nonempty closed convex subset of a uniformly convex Banach space E whose norm is Gâteaux differentiable and let { T n } be a family of mappings of C into itself such that the set of all common fixed points of { T n } is nonempty. We consider a sequence { x n } generated by the hybrid method in mathematical programming. And we give the conditions of { T n } under which { x n } converges strongly to a common fixed point of { T n } and generalize the results of [K. Nakajo, K. Shimoji, W. Takahashi, Strong convergence theorems by the hybrid method for families of nonexpansive mappings in Hilbert spaces, Taiwanese J. Math. 10 (2006) 339–360; S. Ohsawa, W. Takahashi, Strong convergence theorems for resolvents of maximal monotone operators in Banach spaces, Arch. Math. 81 (2003) 439–445].
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2008.10.108