Vol. 65, No. 2, 1976

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 332: 1
Vol. 331: 1  2
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
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