Approximation of some Feller semigroups associated with a modification of Szasz-Mirakjan-Kantorovich operators

We deepen the study of a sequence (C (n) ) (na parts per thousand 1) of positive linear operators, first introduced in [4], that generalize the classical Szasz-Mirakjan-Kantorovich operators. In particular, we present some qualitative properties and an asymptotic formula for such a sequence. Moreover, we prove that, under suitable assumptions, the C (0)-semigroups generated by the second order differential operator on suitable domains of continuous or integrable functions may be approximated by means of iterates of the C (n) 's.