Alternation theory in approximation by polynomials having bounded coefficients

Abstract

LetX be a compact subset of an interval [a, b] (a · b ≥ 0),fa continuous function defined onX, andK={p=Σ ⁿ _j=0 α _j x^j:α _j ≤a _j ≤β _j j=0,1, ...,n} the set of algebraic polynomials having bounded coefficients. The paper gives an alternating characterization theorem of a polynomial of best uniform approximation tof fromK, and a de La Vallée-Poussin theorem.