Fixed point properties for semigroups of nonlinear mappings and amenability

By Anthony To-Ming Lau, Yong Zhang. 2012

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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 $S_1 = $.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1a7a9e3fc25c25f4e0df215604cf8ac4429c977a