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In this paper we are concerned with the study of a long-standing open problem posed by Lau in 1976. This problem is about whether the left amenability property of the space of left uniformly continuous functions of a semitopological semigroup is equivalent to the existence of a common fixed point for every jointly weak* continuous norm nonexpansive action on a nonempty weak* compact convex subset of a dual Banach space. We establish in this paper a positive answer. [ABSTRACT FROM AUTHOR]

In 1976 during a conference in Halifax, A. Lau raised the question on whether left amenability property for a semitopological semigroup is sufficient to ensure the existence of a common fixed point for every jointly weak* continuous norm nonexpansive action on a nonempty weak* compact convex set in a dual Banach space. In this paper we establish a positive answer for discrete semigroups and for strongly left amenable semitopological semigroups. [ABSTRACT FROM AUTHOR]