On Approximation by Reciprocals of Polynomials with Positive Coefficients (Analysis in Theory and Applications, 2013)
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 $l(l≥1)$ times. Zhou Songping has studied the case $l=1$ and $l≥2$ in $L^{p}$ spaces in order of priority. In this paper, we studied the case $l≥2$ in Orlicz spaces by using the function extend, modified Jackson kernel, Hardy-Littlewood maximal function, Cauchy-Schwarz inequality, and obtained the Jackson type estimation.