Vol. 21, No. 3, 1967

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Iterates of Bernstein polynomials

Richard Paul Kelisky and Theodore Joseph Rivlin

Vol. 21 (1967), No. 3, 511–520
Abstract

Bn(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 Bn(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
Authors
Richard Paul Kelisky
Theodore Joseph Rivlin