Kolmogorov problem on a class of multiple monotone functions

Abstract

Necessary and sufficient conditions for positive numbers $M_{k_1}, M_{k_2}, M_{k_3}, M_{k_4}$, $0 = k_1 <k_2<k_3\leq r-2$, $k_4=r$, to guarantee the existence of an $r-1$-monotone function defined on the negative half-line and such that $\|x^{(k_i)}\| = M_{k_i}$, $i=1,2,3,4$ were found