Iterates of bernstein polynomials

Abstract

Bn(f) transforms each function defined on [0,1] into itsBernstein polynomial of degree n. In this paper we studythe convergence of the iterates Bn(k)(f) as k → 蜴 oo both in thecase that k is independent of n and (for polynomial f) whenk is a function of n. © 1967 by Pacific Journal of Mathematics.