Fixed point properties for semigroups of nonlinear mappings and amenability

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• 作者：Anthony T.-M. Lau ; Yong Zhang
• 关键词：Fixed point property ; Nonexpansive mappings ; L-embedded convex set ; Weakly compact convex set ; Left reversible semigroup ; Weakly almost periodic ; Invariant mean
• 刊名：Journal of Functional Analysis
• 出版年：2012
• 出版时间：15 November, 2012
• 年：2012
• 卷：263
• 期：10
• 页码：2949-2977
• 全文大小：301 K

文摘

In this paper we study fixed point properties for semitopological semigroup of nonexpansive mappings on a bounded closed convex subset of a Banach space. We also study a Schauder fixed point property for a semitopological semigroup of continuous mappings on a compact convex subset of a separated locally convex space. Such semigroups properly include the class of extremely left amenable semitopological semigroups, the free commutative semigroup on one generator and the bicyclic semigroup .