Best uniform polynomial approximation of some rational functions

In this research paper using the Chebyshev expansion, we explicitly determine the best uniform polynomial approximation out of PqnPqn (the space of polynomials of degree at most qnqn) to a class of rational functions of the form 1/(Tq(a)±Tq(x))1/(Tq(a)±Tq(x)) on [−1,1][−1,1], where Tq(x)Tq(x) is the first kind of Chebyshev polynomial of degree qq and a2>1a2>1. In this way we give some new theorems about the best approximation of this class of rational functions. Furthermore we obtain the alternating set of this class of functions.