Approximation by Bernstein polynomials at the points of discontinuity of the derivatives (Q1033966)

The paper is devoted to extension of asymptotic formulas for the deviations of Bernstein polynomials from differentiable functions to the case in which the highest derivative of the function has a discontinuity of the first kind at the point under study [see \textit{G. G. Lorentz}, Bernstein Polynomials. New York, NY: Chelsea Publishing. (1986; Zbl 0989.41504)], (Section 1.6.1). It is shown here that in the asymptotic formulas for the deviations of Bernstein polynomials from functions at the points of discontinuity of the first kind of the highest even-order derivative, the value of such a derivative can be replaced by the half-sum of its limits on the right and on the left.