应用数学2012，Vol.25Issue(3)：638-647,10.
渐近非扩张非自映射的收敛定理
Convergence Theorems for Nonself Asymptotically Nonexpansive Mappings
摘要
Abstract
Suppose that K is a nonempty closed convex subset of a real uniformly convex Banach space E with P as a nonexpansive retraction.Let T1,T2,T3: K → E be three nonself asymptotically nonexpansive mappings with sequences {hn},{ln),{kn} (C) [1,∞) such that Σ∞n=1 (hn-1) ＜ ∞,∑∞n=1(ln-1) ＜ ∞ and Σn=1(kn-1) ＜∞,respectively and F =F(T1) ∩ F(T2) ∩ F(T3) ={x ∈ K: T1x =T2x =T3x} ≠ φ.Define the sequence {xn} by {x1 ∈ K,xn+1 =P((1-αn)xn + αnT1 (PT1)n-1 yn),yn=P((1-βn)xn+βnT2(PT2)n+1zn),zn =P((1-γn)xn +γnT3(PT3)n-1xn),(V) n ≥ 1,where {αn },{βn } and { γn } are three real sequences in [ε,1-ε] for some ε ＞ 0.(i) If one of T1,T2 and T3 is completely continuous or demicompact,then strong convergence of {xn } to some q ∈ F are obtained.(ii) If E has a Fréchet differentiable norm or satisfying Opial's condition or its dual E* has the Kadec-Klee property,then weak convergence of {xn } to some q ∈ F are obtained.关键词
一致凸Banach空间/渐近非扩张非自映射/强收敛/弱收敛/公共不动点Key words
Uniformly convex Banach space/ Nonself asymptotically nonexpansive mapping/ Strong convergence/ Weak convergence/ Common fixed point分类
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阚绪周,郭伟平..渐近非扩张非自映射的收敛定理[J].应用数学,2012,25(3):638-647,10.基金项目
Foundation item:Supported by the Foundation for Major Subject of Suzhou University of Science and Technology （）
