On uniform approximation by some classical Bernstein-type operators

Abstract

We investigate the functions for which certain classical families of operators of probabilistic type over noncompact intervals provide uniform approximation on the whole interval. The discussed examples include the Szász operators, the Szász–Durrmeyer operators, the gamma operators, the Baskakov operators, and the Meyer–König and Zeller operators. We show that some results of Totik remain valid for unbounded functions, at the same time that we give simple rates of convergence in terms of the usual modulus of continuity. We also show by a counterexample that the result for Meyer–König and Zeller operators does not extend to Cheney and Sharma operators.