Rate of pointwise convergence of Bernstein polynomials for some absolutely continuous functions (Q1364819)

Let \(f\) be a complex valued function bounded on [0,1] and \{\(B_n f\)\} be the sequence of Bernstein polynomials associated with \(f\). Considering an absolutely continuous function \(f\) having the derivative \(f\)' equivalent to a function \(\phi\) bounded on [0,1], the author estimates the rate of convergence of \{\(B_n f(x)\)\}, \(x \in \) [0,1] where \(\phi(x+ )\) and \(\phi(x- )\) exist. In particular an improved version of the estimate given in \textit{R. Bojanic} and \textit{F. Cheng} [J. Math. Anal. Appl. 141, No. 1, 136-151 (1989; Zbl 0688.41008)]\ is obtained.