Shape preserving properties of some positive linear operators on unbounded intervals

In this paper we study some shape preserving properties of particular positive linear operators acting on spaces of continuous functions defined on the interval [0, + infinity[, which are strongly related to the semigroups generated by a large class of degenerate elliptic second order differential operators. We study the conditions under which these operators leave invariant the class of increasing functions, as well as the class of convex functions and Holder continuous functions. As a consequence, we derive some regularity results concerning the related semigroups. (C) 1998 Academeic Press.