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CLC number: O177.91
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Received: 2007-03-13
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Viscosity approximation methods with weakly contractive mappings for nonexpansive mappings
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WANG Ya-qin. Viscosity approximation methods with weakly contractive mappings for nonexpansive mappings[J]. Journal of Zhejiang University Science A, 2007, 8(10): 1691-1694.
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author="WANG Ya-qin",
journal="Journal of Zhejiang University Science A",
volume="8",
number="10",
pages="1691-1694",
year="2007",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2007.A1691"
}
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%T Viscosity approximation methods with weakly contractive mappings for nonexpansive mappings
%A WANG Ya-qin
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%D 2007
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2007.A1691
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T1 - Viscosity approximation methods with weakly contractive mappings for nonexpansive mappings
A1 - WANG Ya-qin
J0 - Journal of Zhejiang University Science A
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EP - 1694
%@ 1673-565X
Y1 - 2007
PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2007.A1691
Abstract: Let K be a closed convex subset of a real reflexive Banach space E, T:K→K be a nonexpansive mapping, and f:K→K be a fixed weakly contractive (may not be contractive) mapping. Then for any t∈(0, 1), let xt(K be the unique fixed point of the weak contraction x↦tf(x)+(1−t)Tx. If T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E*, then it is shown that {xt} converges to a fixed point of T as t→0. The results presented here improve and generalize the corresponding results in (Xu, 2004).
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