Alternation theory in approximation by polynomials having bounded coefficients (Q1343506)

Let \(X\) be a compact subset of an interval \([a, b]\), where \(ab\geq 0\), \(f\) a continuous function defined on \(X\) and \[ K= \Biggl\{ p= \sum^ n_{j= 0} a_ j x^ j\mid \alpha_ j\leq a_ j\leq \beta_ j,\;j= 0,\dots,n\Biggr\} \] the set of algebraic polynomials having bounded coefficients. In this paper the author points out an alternating characterization theorem of a polynomial of best uniform approximation to \(f\) from \(K\), and de la Vallée-Poussin theorem.