%0 Journal Article %T SEMIGROUP ACTIONS , WEAK ALMOST PERIODICITY, AND INVARIANT MEANS %J Journal of Sciences, Islamic Republic of Iran %I University of Tehran %Z 1016-1104 %D 1990 %\ 03/01/1990 %V 1 %N 2 %P - %! SEMIGROUP ACTIONS , WEAK ALMOST PERIODICITY, AND INVARIANT MEANS %R %X Let S be a topological semigroup acting on a topological space X. We develop the theory of (weakly) almost periodic functions on X, with respect to S, and form the (weakly) almost periodic compactifications of X and S, with respect to each other. We then consider the notion of an action of Son a Banach space, and on its dual, and after defining S-invariant means for such a space, we give a result concerning the existence of such means, and apply it to prove the existence of a G-invariant mean on the space of weakly almost periodic functions defined on a topological space on which a topological group G acts. %U https://jsciences.ut.ac.ir/article_31393_97dba61c61ae0f28f3f15144dcd3ab92.pdf