Asymptotic Constant in Approximation of Twice Differentiable Functions by a Class of Positive Linear Operators

An asymptotic relation is established between the rate of approximation of functions from space $C^2[0,1]$ by a general class of positive linear operators and a generalized second order Ditzian–Totik modulus. In addition, it is shown by a counterexample that this asymptotic relation is not true for general continuous functions.