Local and global approximation theorems for positive linear operators (Q1268703)

In this paper the author establishes some local and global approximation theorems for positive linear operators using Ditzian-Totik modulus of smoothness of second order [\textit{Z. Ditzian} and \textit{V. Totik} ``Moduli of smoothness'' (1987; Zbl 0666.41001)] whereby the step-weights \(\varphi\) are functions whose squares are concave. Both direct and converse theorems are given. In particular the author obtains some estimates for the Szász-Mirakyan, Kantorovich-type and Durrmeyer-type operators or for a class of Bernstein-type operators which are ``not far away'' from the original Bernstein operators.