On the strong convergence of the Cèsaro means of contractions in Banach spaces
On the strong convergence of the Cèsaro means of contractions in Banach spaces
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论巴纳赫空间中塞萨罗收缩方法的强收敛性
DOI：
10.3792/pjaa.56.245
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发表时间：
1980
期刊：
影响因子：
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通讯作者：
I. Miyadera
中科院分区：
文献类型：
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作者：
Kazuo Kobayasi;I. Miyadera
1 o介绍。在本文中，X表示一个一致凸Banach空间，C是X的一个非空闭凸子集。映射T ' CC称为C上的收缩，或T ' CC (C)上的收缩，如果IITx—Tyll<=llx—yl[对于每一个X， y e C]。如果T(0)—I （C上的恒等式），T(T +s)=T(T) T(s)， T(T) eCont(C)对于T， so和lim_0/ T(T) x-x对于每一个xe C，映射T的不动点集合记作F(T)。本文的目的是证明下列（非线性）平均遍历定理。定理1。设T = T (C), x = C， F(T)=/= 0。如果lim Tnx—Tn/xll一致存在于i- 1,2，…，则存在一个元素F(T)满足
1o Introduction. Throughout this paper X denotes a uniformly convex Banach space and C is a nonempty closed convex subset of X. A mapping T" CC is called a contraction on C, or T e Cont (C) if IITx--Tyll<=llx--yl[ for every x, y e C. A family (T(t); t_0)of mappings from C into itself is called a contraction semi-group on C if T(0) --I (the identity on C), T(t+s)=T(t)T(s), T(t)eCont(C) for t, s0 and lim_0/ T(t)x-x for every x e C. The set of fixed points of a mapping T will be denoted by F(T). The purpose of this paper is to prove the following (nonlinear) mean ergodic theorems. Theorem 1. Let T e Cont (C), x e C and F(T)=/=O. If lim Tnx --Tn/xll exists uniformly in i-l, 2, ..., then there exists an element y e F(T) such that