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

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. Dnepropetrovsk University, Dnepropetrovsk. Translated from Ukrainskii Matematicheskii Zhurnal Vol. 51, No. 1, pp. 117–119, January, 1999.