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ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2007, Vol. 8 Issue (10): 1691-1694    DOI: 10.1631/jzus.2007.A1691
Computational Mathematics     
Viscosity approximation methods with weakly contractive mappings for nonexpansive mappings
WANG Ya-qin
Mathematics and Sciences College, Shanghai Normal University, Shanghai 200234, China
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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).

Key words： Identity      Signature      Lattice      Number theory research unit (NTRU)     
Received: 13 March 2007     
CLC:  O177.91  
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WANG Ya-qin. Viscosity approximation methods with weakly contractive mappings for nonexpansive mappings. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2007, 8(10): 1691-1694.

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http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.2007.A1691     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2007/V8/I10/1691

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