Properties of best approximation with interpolatory and restricted range side conditions

AbstractAn alternation property of polynomials of best uniform approximation to a function | ϵ C[a, b] having restricted ranges of some of their derivatives is proven. For this purpose, the problem of best uniform approximation to continuous functions by polynomials having restricted ranges and satisfying interpolatory conditions on their derivatives is discussed. The method is an improved version of the one used in [3] and provides an easily computed lower bound for the number of alternations