The Bernstein inequality for some operator of the Szász-Mirakjan type

Abstract

We give the Bernstein inequality for derivatives of the operators of the Szász-Mirakjan type introduced and studied in [3-6] for functions of one and several variables, continuous and having the polynomial or exponential growth at infinity. In §1 we consider these operators for functions of one variable. In §2 we investigate some analogues of these operators for functions of two variables. The present inequalities are very important for approximation properties of the considered operators.