@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} }