A <IMG ALIGN=BOTTOM >-functional and the rate of convergence of some linear polynomial operators期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

A -functional and the rate of convergence of some linear polynomial operators

Authors:	Z. Ditzian

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

Abstract:	We show that the -functional $begin{equation}K(f,n^{-2} )_{p}=inf _{gin C^{2}[-1,1]} bigl (\|f-g\|_p+n^{-2} \|P(D) g\|_p bigr ), end{equation}$ where $P(D) =frac {d}{dx} (1-x^{2})frac {d}{dx}$ , 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.

Keywords:	Linear polynomial approximation near best polynomial approximation

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