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We use a method similar to ultraproducts to study the common fixed point of aleft reversible semitopological semigroup acting on a Banach space. As anapplication, we prove a Bruck-type theorem for nearly uniformly convex Banachspaces to the effect that such spaces have weak fixed point property for leftreversible semigroups.

An ultraproduct method via left reversible semigroups to study Bruck's generalized conjecture