(Springer, 2022-12-16) Adell, José A.; Cárdenas-Morales, Daniel
This paper deals with the approximation of continuous functions by the classical Szász–
Mirakyan operator. We give new bounds for the constant in front of the second order
Ditzian–Totik modulus of smoothness in direct inequalities. Asymptotic and non asymptotic results are stated. We use both analytical and probabilistic methods, the latter involving
the representation of the operators in terms of the standard Poisson process. A smoothing
technique based on a modification of the Steklov means is also applied.
