Vol. 65, No. 2, 1976

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Negative theorems on generalized convex approximation

Eli Aaron Passow and John A. Roulier

Vol. 65 (1976), No. 2, 437–447
Abstract

In this paper we show that there exist functions f C[1,+1] with all (r + 1)-st order divided differences uniformly bounded away from zero for r fixed (f[x0,x1,,xr+1] δ > 0 for fixed δ and all sets x0 < < xr+1 in [1,+1]), for which infinitely many of the polynomials of best approximation to f do not have nonnnegative (r + 1)-st derivatives on [1,+1].

Mathematical Subject Classification 2000
Primary: 41A50
Milestones
Received: 13 November 1975
Revised: 15 March 1976
Published: 1 August 1976
Authors
Eli Aaron Passow
John A. Roulier