A Quantitative Variant of Voronovskaja’s Theorem

A general quantitative Voronovskaja theorem for Bernstein operators is given which bridges the gap between such estimates in terms of the least concave majorant of the first order modulus of continuity and the first order Ditzian–Totik modulus with classical weight \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi(x) = \sqrt {x(1 - x)}$$\end{document}.