2018
Том 70
№ 9

All Issues

On the dependence of the norm of a multiply monotone function on the norms of its derivatives

Bondarenko A. R., Kovalenko O. V.


Abstract

We establish necessary and sufficient conditions for a system of positive numbers Mk1 , Mk2 , Mk3 , Mk4 , 0 = k1 < < k2 < k3 \leq r 3, k4 = r guaranteeing the existence of an (r 2)-monotone function x on the half line such that \| x(ki)\| \infty = Mki , i = 1, 2, 3, 4.

Citation Example: Bondarenko A. R., Kovalenko O. V. On the dependence of the norm of a multiply monotone function on the norms of its derivatives // Ukr. Mat. Zh. - 2018. - 70, № 7. - pp. 867-875.