ERGODIC PROPERTIES OF A PARTICULAR AMENABLE SEMIGROUP OF MAPPINGS IN A BANACH SPACE
Shahram Saeidi · 2009
We prove that if S is an amenable semigroup and ' = {Tt : t 2 S} is a semigroup of mappings on a nonempty weakly compact, convex subset C of a Banach space E, generated by {Tt : t 2 A S}, such that for each t 2 A, Tt is of type ( ) and D(coF1/n(Tt),F(Tt)) ! 0, as n ! 1, then F(') of common fixed points of ' is nonempty and there exists a retraction P of type ( ) from C onto F('), such that PTt = TtP = P for each t 2 S, and Px 2 co{Ttx : t 2 S} for each x 2 C. The compactness of C concludes such imposed conditions.