Strong converse inequality for linear combinations of Szász-Mirakjan operators (Q2054277)

By means of the regularity of the differential operators generated by the Szász-Mirakjan operators, this paper further investigates the relation between the approximation rate of the linear combinations of the Sász-Mirakjan operators and the smoothness of the approximated function. The upper and lower bounds are given, which are of the same order, of the approximation of the linear combinations of these operators. The results under certain conditions include the direct theorem, the inverse theorem and the saturation results.