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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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Published in: | Nonlinear analysis 2009-08, Vol.71 (3), p.812-818 |
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Main Authors: | , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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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]. |
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ISSN: | 0362-546X 1873-5215 |
DOI: | 10.1016/j.na.2008.10.108 |