A nonlinear ergodic theorem for a reversible semigroup of nonexpansive mappings in a Hilbert space
A nonlinear ergodic theorem for a reversible semigroup of nonexpansive mappings in a Hilbert space
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DOI：
10.1090/s0002-9939-1986-0831386-4
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发表时间：
1986
期刊：
影响因子：
--
通讯作者：
W. Takahashi
中科院分区：
文献类型：
--
作者：
W. Takahashi
让C是一个非空的希尔伯特空间的闭凸子集,年代右可逆semitopological半群,S = {t E S Tt:}的连续表示年代扩张映射在一个封闭的凸子集C到C,和F (S)的公共不动点集的映射Tt, t C S .然后我们处理的存在扩张收缩的P C到F (S), PTt = TtP = P为每个t E S和Px是关闭的凸包中包含{Ttx: t C S}为每个x C C。
Let C be a nonempty closed convex subset of a Hilbert space, S a right reversible semitopological semigroup, S = {Tt: t E S} a continuous representation of S as nonexpansive mappings on a closed convex subset C into C, and F(S) the set of common fixed points of mappings Tt, t C S. Then we deal with the existence of a nonexpansive retraction P of C onto F(S) such that PTt = TtP = P for each t E S and Px is contained in the closure of the convex hull of {Ttx: t c S} for each x C C.