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Asymptotic Property of Approximation to xαsgnx by Newman Type Operators

Asymptotic Property of Approximation to $x^α$sgn$x$ by Newman Type Operators

Year:    2011

Author:    Qian Zhan, Shusheng Xu

Communications in Mathematical Research , Vol. 27 (2011), Iss. 3 : pp. 193–199

Abstract

The approximation of |x| by rational functions is a classical rational problem. This paper deals with the rational approximation of the function xαsgnx, which equals |x| if α=1. We construct a Newman type operator rn(x) and show min|x|1{|xαsgnxrn(x)|}Cnα2e2nα, where C is a constant depending on α.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2011-CMR-19082

Communications in Mathematical Research , Vol. 27 (2011), Iss. 3 : pp. 193–199

Published online:    2011-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    7

Keywords:    rational approximation asymptotic property Newman type operator.

Author Details

Qian Zhan Email

Shusheng Xu Email