Weighted approximation of functions by Szász--Mirakyan-type operators

Abstract

We give error estimates for the weighted approximation of func- tions with singularities at the endpoints on the semiaxis by some modifications of Szasz-Mirakyan operators. To do so, we define a new weighted modulus of smoothness and prove its equivalence to the weighted K-functional. Also, the class of functions for which the modified Szasz-Mirakyan operator can be defined will be extended to a much wider set than for the original operator.