On exact constants in inequalities for norms of derivatives on a finite segment

Abstract

We prove that, in an additive inequality for norms of intermediate derivatives of functions defined on a finite segment and equal to zero at a given system of points, the least possible value of a constant coefficient of the norm of a function coincides with the exact constant in the corresponding Markov-Nikol'skii inequality for algebraic polynomials that are also equal to zero at this system of points.