Iterates of Bernstein polynomials

Richard Paul Kelisky and Theodore Joseph Rivlin

Vol. 21 (1967), No. 3, 511–520

DOI: 10.2140/pjm.1967.21.511

Abstract

B_n(f) transforms each function defined on [0,1] into its Bernstein polynomial of degree n. In this paper we study the convergence of the iterates B_n^(k)(f) as k →∞ both in the case that k is independent of n and (for polynomial f) when k is a function of n.

Mathematical Subject Classification

Primary: 41.15

Milestones

Received: 6 October 1965

Published: 1 June 1967