Iterative Approximation to Convex Feasibility Problems in Banach Space

Shih-Sen Chang; Jen-Chih Yao; Jong Kyu KimLi Yang

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Iterative Approximation to Convex Feasibility Problems in Banach Space

机译：Iterative Approximation to Convex Feasibility Problems in Banach Space

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The convex feasibility problem (CFP) of finding a point in the nonempty intersection ∩i=1NCi is considered, where N≥1 is an integer and each Ci is assumed to be the fixed point set of a nonexpansive mapping Ti:E→E, where E is a reflexive Banach space with a weakly sequentially continuous duality mapping. By using viscosity approximation methods for a finite family of nonexpansive mappings, it is shown that for any given contractive mapping f:C→C, where C is a nonempty closed convex subset of E and for any given x0∈C the iterative scheme xn+1=Pαn+1f(xn)+(1-αn+1)Tn+1xn is strongly convergent to a solution of (CFP), if and only if {αn} and {xn} satisfy certain conditions, where αn∈(0,1),Tn=Tn(modN) and P is a sunny nonexpansive retraction of E onto C. The results presented in the paper extend and improve some recent results in Xu (2004), O'Hara et al. (2003), Song and Chen (2006), Bauschke (1996), Browder (1967), Halpern (1967), Jung (2005), Lions (1977), Moudafi (2000), Reich (1980), Wittmann (1992), Reich (1994).

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《Fixexd point theory and applications》 |2007年第1期|46797-1-46797-19-0|共19页
作者
Shih-Sen Chang; Jen-Chih Yao; Jong Kyu KimLi Yang;
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作者单位

Department of Mathematics Education, Kyungnam Unviersity, Masan 631-701, South Korea;

Department of Mathematics, Southwest Unviersity of Science and Technology, Mianyang, Sichuan 621010, China;

Department of Mathematics, Yibin University, Yibin, Sichuan 644007, ChinaDepartment of Applied Mathematics, National Sun Yat-Sen University Kaohsiung 804, Twiwan;

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正文语种英语
中图分类数学;
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Iterative Approximation to Convex Feasibility Problems in Banach Space

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