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Volume 29, Issue 2
On Approximation by Reciprocals of Polynomials with Positive Coefficients

Lian Hai & Garidi Wu

Anal. Theory Appl., 29 (2013), pp. 149-157.

Published online: 2013-06

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  • Abstract

In order to study the approximation by reciprocals of polynomials with real coefficients, one always assumes that the approximated function has a fixed sign on the given interval. Sometimes, the approximated function is permitted to have finite sign changes, such as $l(l\geq1)$ times. Zhou Songping has studied the case $l=1$ and $l\geq2$ in $L^{p}$ spaces in order of priority. In this paper, we studied the case $l\geq2$ in Orlicz spaces by using the function extend, modified Jackson kernel, Hardy-Littlewood maximal function, Cauchy-Schwarz inequality, and obtained the Jackson type estimation.

  • AMS Subject Headings

41A17, 41A20

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COPYRIGHT: © Global Science Press

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@Article{ATA-29-149, author = {Lian Hai , and Wu , Garidi}, title = {On Approximation by Reciprocals of Polynomials with Positive Coefficients}, journal = {Analysis in Theory and Applications}, year = {2013}, volume = {29}, number = {2}, pages = {149--157}, abstract = {

In order to study the approximation by reciprocals of polynomials with real coefficients, one always assumes that the approximated function has a fixed sign on the given interval. Sometimes, the approximated function is permitted to have finite sign changes, such as $l(l\geq1)$ times. Zhou Songping has studied the case $l=1$ and $l\geq2$ in $L^{p}$ spaces in order of priority. In this paper, we studied the case $l\geq2$ in Orlicz spaces by using the function extend, modified Jackson kernel, Hardy-Littlewood maximal function, Cauchy-Schwarz inequality, and obtained the Jackson type estimation.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2013.v29.n2.6}, url = {http://global-sci.org/intro/article_detail/ata/4523.html} }
TY - JOUR T1 - On Approximation by Reciprocals of Polynomials with Positive Coefficients AU - Lian Hai , AU - Wu , Garidi JO - Analysis in Theory and Applications VL - 2 SP - 149 EP - 157 PY - 2013 DA - 2013/06 SN - 29 DO - http://doi.org/10.4208/ata.2013.v29.n2.6 UR - https://global-sci.org/intro/article_detail/ata/4523.html KW - Approximation, polynomial, Steklov function, Orlicz space, modulus of continuity. AB -

In order to study the approximation by reciprocals of polynomials with real coefficients, one always assumes that the approximated function has a fixed sign on the given interval. Sometimes, the approximated function is permitted to have finite sign changes, such as $l(l\geq1)$ times. Zhou Songping has studied the case $l=1$ and $l\geq2$ in $L^{p}$ spaces in order of priority. In this paper, we studied the case $l\geq2$ in Orlicz spaces by using the function extend, modified Jackson kernel, Hardy-Littlewood maximal function, Cauchy-Schwarz inequality, and obtained the Jackson type estimation.

Lian Hai , and Wu , Garidi. (2013). On Approximation by Reciprocals of Polynomials with Positive Coefficients. Analysis in Theory and Applications. 29 (2). 149-157. doi:10.4208/ata.2013.v29.n2.6
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