论文标题
非绑定集上非线性映射的半群的固定点属性
Fixed point properties for semigroups of nonlinear mappings on unbounded sets
论文作者
论文摘要
W. Ray的一个众所周知的结果断言，如果$ c $是希尔伯特空间的无限凸子集，那么没有一个没有固定点的$ t $：$ c \ to c $。在本文中，我们为封闭的凸出子集$ c $ a Hilbert space的semopological Semogological semigroup $ s $ s $ s $建立了一些常见的固定点属性，假设有一个有界轨道的c $ in Cove $ c \ in C $ c $ in Bigned Orbit，并且假设某些$ C_B（S）的子空间（S）$ C_B（S）$ c_b（s）均具有左开启的均值。左不变平均值（或不变性）是对冯·诺伊曼（Von Neumann）在1929年对半群和群体的谐波分析中的重要概念，\ cite {neu}，并于1957年按白天正式化\ cite {day}。在我们的调查中，我们使用了S. Atsushiba和W. Takahashi最近提出的共同有吸引力的观点。
A well-known result of W. Ray asserts that if $C$ is an unbounded convex subset of a Hilbert space, then there is a nonexpansive mapping $T$: $C\to C$ that has no fixed point. In this paper we establish some common fixed point properties for a semitopological semigroup $S$ of nonexpansive mappings acting on a closed convex subset $C$ of a Hilbert space, assuming that there is a point $c\in C$ with a bounded orbit and assuming that certain subspace of $C_b(S)$ has a left invariant mean. Left invariant mean (or amenability) is an important notion in harmonic analysis of semigroups and groups introduced by von Neumann in 1929 \cite{Neu} and formalized by Day in 1957 \cite{Day}. In our investigation we use the notion of common attractive points introduced recently by S. Atsushiba and W. Takahashi.
