On Approximation by Reciprocals of Polynomials with Positive Coefficients

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.