APPROXIMATION BY RATIONAL FUNCTIONS WITH POLYNOMIALS OF POSITIVE COEFFICIENTS AS THE DENOMINATORS

摘要

The present paper proves that if f(x) ∈ C[0,1], changes its sign exactly l times at 0 ＜ y1 ＜ y2 ＜y1＜1 in(0,1),then there exists a pn (x)пn(+),such that |f(x)-p(x)/pn(x)|≤ Cωφ(f,n-1/2),where ρ(x) is defined by ρ(x)=l∏i=1(x - yi), if f(x) ≥ 0 for x ∈ (yl, 1),-1∏i=1(x-yi), iff(x) ＜ 0 for x ∈ (y1,1).which improves and generalizes the result of [7].