Integral-type operators on continuous function spaces on the real line

In this paper we introduce some new sequences of positive linear operators, acting on a sufficiently large space of continuous functions on the real line, which generalize Gauss-Weierstrass operators. We study their approximation properties and prove an asymptotic formula that relates such operators to a second order elliptic differential operator of the form [email protected][email protected]^'^'[email protected]^'[email protected] Shape-preserving and regularity properties are also investigated.