Journal of Zhejiang University SCIENCE A
ISSN 1673-565X(Print), 1862-1775(Online), Monthly

2007   Vol. 8   No. 10   p. 1691~1694

Viscosity approximation methods with weakly contractive mappings for nonexpansive mappings

WANG Ya-qin

(Mathematics and Sciences College, Shanghai Normal University, Shanghai 200234, China)
E-mail: wangyaqin0579@sohu.com
Received Mar. 13, 2007 revision accepted Apr. 29, 2007

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 x_t(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 {x_t} converges to a fixed point of T as t(0. The results presented here improve and generalize the corresponding results in (Xu, 2004).

Key words: Viscosity approximation methods, Weakly contractive mapping, Fixed point, Weakly sequentially continuous duality mapping
doi:10.1631/jzus.2007.A1691             CLC number: O177.91

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