Iteration Semigroups with Generalized Convex, Concave and Affine Elements

摘要

Given continuous functions and of two variables, it is shown that if in a continuous iteration semigroup with only -convex or -concave elements there are two -affine elements, then and every element of the semigroup is -affine. Moreover, all functions in the semigroup either are -convex or -concave.