In this paper, we introduce a concept of fixed point property for a semigroup S called A-fixed point property, where A is a non-empty subset of S. Also, the relationship between A-amenability and A-fixed point property is investigated.
In this paper, we present a new concept of inner amenability for a non-empty arbitrary subset A of discrete semigroup S called A-inner amenablility. This condition is considerably weaker than ordinary inner amenability. Further, we show some relationships between this version of inner amenability and Følner's condition.
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