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.