On Some Inequalities of Series of Positive Terms.
We consider iteration of arithmetic and power means and discuss methods for determining their limit. These means appear naturally in connection with some problems in homogenization theory.
Let be a disjoint iteration semigroup of diffeomorphisms mapping a real open interval onto . It is proved that if has a dense orbit possesing a subset of the second category with the Baire property, then for some diffeomorphism of onto the set of all reals . The paper generalizes some results of J.A.Baker and G.Blanton [3].