A -functional and the rate of convergence

of some linear polynomial operators

Author:
Z. Ditzian

Journal:
Proc. Amer. Math. Soc. **124** (1996), 1773-1781

MSC (1991):
Primary 41A10, 41A35, 41A25

DOI:
https://doi.org/10.1090/S0002-9939-96-03219-4

MathSciNet review:
1307511

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that the -functional

where , is equivalent to the rate of convergence of a certain linear polynomial operator. This operator stems from a Riesz-type summability process of expansion by Legendre polynomials. We use the operator above to obtain a linear polynomial approximation operator with a rate comparable to that of the best polynomial approximation.

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Additional Information

**Z. Ditzian**

Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada T6G 2G1

DOI:
https://doi.org/10.1090/S0002-9939-96-03219-4

Keywords:
Linear polynomial approximation,
near best polynomial approximation

Received by editor(s):
April 6, 1994

Received by editor(s) in revised form:
November 18, 1994

Additional Notes:
Supported by NSERC grant A4816 of Canada.

Communicated by:
J. Marshall Ash

Article copyright:
© Copyright 1996
American Mathematical Society