摘要
设C是具有Frechet可微范数的一致凸Banach空间E的非空子集,T={T(t):t∈S}是依中间意义渐近非扩张的一族C上的自映象,F是F(T)的子集,其中,F(T)表示族T={T(t):t∈S}的所有公共不动点之集。本文证明了,如果u:S→C是T={T(t):t∈S}的几乎轨道,并满足下列条件:(a)ω_w({u(t):t∈S}) F;(b)({u(t):t∈S}∪F) C。则(i)F=且||u(t)||=∞;或(ii)F≠且u(t)弱收敛到F的一个元。
In this paper, let C be a nonempty subset of a uniformly convex Banach space E with a Frechet differentiable norm, let T = {T(t) : t ∈ S} be a family of self-mappings on C which is asymptotically nonexpansive in the intermediate sense, and let F be contained in F(T) which denotes the set of all common fixed points of T = (T(t) : t ∈ S}. It is shown that if u : S → C is an almost-orbit of T = {T(t) : t ∈ S} satisfying the conditions: (a) uw({u(t) : t ∈ 5}) F, and (b) co({u(t) : t ∈ 5} ∪ F) C, then, either (i) F = and lim ||u(t)|| = ∞ or (ii) F ≠ and u(t) converges weakly to an element of F.
出处
《数学年刊（A辑）》
CSCD
北大核心
2003年第4期459-466,共8页
Chinese Annals of Mathematics
基金
高等学校优秀青年教师教学和科研奖励基金
国家自然科学基金(No.19801023)
关键词
几乎轨道
弱收敛
渐近非扩张族
不动点
一致凸BANACH空间
Almost-orbit, Weak convergence, Asymptotically nonexpansive families, Fixed point, Uniformly convex Banach space
