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How to Recognize Nonexpansive Mappings and Isometric Mappings 被引量:1
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作者 Guang Gui DING Yu Mei MA 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第10期1959-1966,共8页
In two real Banach spaces, we shall present two conditions, under one of which each nonexpansive mapping must be an isometry.
关键词 nonexpansive mapping smooth point weak*-compact set
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Weak Convergence Theorems for Nonself Mappings 被引量:1
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作者 LIU YONG-QUAN GUO WEI-PING Ji You-qing 《Communications in Mathematical Research》 CSCD 2015年第1期15-22,共8页
Let E be a real uniformly convex and smooth Banach space, and K be a nonempty closed convex subset of E with P as a sunny nonexpansive retraction. Let T1, T2 : K → E be two weakly inward nonself asymptotically nonex... Let E be a real uniformly convex and smooth Banach space, and K be a nonempty closed convex subset of E with P as a sunny nonexpansive retraction. Let T1, T2 : K → E be two weakly inward nonself asymptotically nonexpansive mappings with respect to P with a sequence {kn^(i)} [1, ∞) (i = 1, 2), and F := F(T1)∩ F(T2) ≠ 0. An iterative sequence for approximation common fixed points of the two nonself asymptotically nonexpansive mappings is discussed. If E has also a Frechet differentiable norm or its dual E^* has Kadec-Klee property, then weak convergence theorems are obtained. 展开更多
关键词 asymptotically nonexpansive nonself-mapping weak formly convex Banach space common fixed point smooth Banach convergence urnspace
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Strong convergence theorems for nonexpansive semi-groups in Banach spaces 被引量:2
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作者 张石生 杨莉 柳京爱 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第10期1287-1297,共11页
Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established. Results presented in the paper not only extend and improve the co... Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established. Results presented in the paper not only extend and improve the corresponding results of ShiojiTakahashi, Suzuki, Xu and Aleyner-Reich, but also give a partially affirmative answer to the open questions raised by Suzuki and Xu. 展开更多
关键词 nonexpansive semi-group demi-closed principle common fixed point uni-formly smooth Banach space weakly continuous normalized duality mapping
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Strong Convergence Theorems of Viscosity Approximation for Accretive Operators 被引量:4
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作者 YAN Li Xia ZHOU Hai Yun 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2008年第3期579-588,共10页
Let E be a real Banach space and let A be an m-accretive operator with a zero. Define a sequence {x_n} as follows:x_n+1=α_nf(x_n)+(1-α_n)J_r_n x_n,where {α_n},{r_n} are sequences satisfying certain conditions,and J... Let E be a real Banach space and let A be an m-accretive operator with a zero. Define a sequence {x_n} as follows:x_n+1=α_nf(x_n)+(1-α_n)J_r_n x_n,where {α_n},{r_n} are sequences satisfying certain conditions,and J_r denotes the resolvent(I+rA)^(-1)for r>1.Strong convergence of the algorithm {x_n} is obtained provided that E either has a weakly continuous duality map or is uniformly smooth. 展开更多
关键词 fixed point nonexpansive mapping m-accretive operator viscosity approximation weakly continuous duality map uniformly smooth Banach space.
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