Islamic Azad University, Rasht BranchIranian Journal of Optimization2588-57237120150101A method to obtain the best uniform polynomial approximation for the family of rational functionA method to obtain the best uniform polynomial approximation for the family of rational function753766526833ENM. A.Fariborzi AraghiDepartment of Mathematics, Islamic Azad university, Central Tehran branchF.FroozanfarMs.student of Mathematics, Islamic Azad university, Kermanshah branch, Kermanshah, IranJournal Article20140920In this article, by using Chebyshev’s polynomials and Chebyshev’s expansion, we obtain the best uniform polynomial approximation out of P<sub>2n</sub> to a class of rational functions of the form (ax<sup>2</sup>+c)<sup>-1</sup> on any non symmetric interval [d,e]. Using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax<sup>2</sup>+bx+c)<sup>-1</sup> for both cases b<sup>2</sup>-4ac L 0 and b<sup>2</sup>-4ac G 0. <br /> http://ijo.iaurasht.ac.ir/article_526833_88e10aa100f0f18787a31e1a8998c050.pdf