Let and be nonnegative integers such that . The convex cone of all functions on an arbitrary interval whose derivatives of orders are nondecreasing is characterized. A simple description of the convex cone dual to is given. In particular, these results are useful in, and were motivated by, applications in probability. In fact, the results are obtained in a more general setting with certain generalized derivatives of of the th order in place of . Somewhat similar results were previously obtained, in terms of Tchebycheff–Markov systems, in the case when the left endpoint of the interval is finite, with certain additional integrability conditions; such conditions fail to hold in the mentioned applications. Development of substantially new methods was needed to overcome the difficulties.
"Convex cones of generalized multiply monotone functions and the dual cones." Banach J. Math. Anal. 10 (4) 864 - 897, October 2016. https://doi.org/10.1215/17358787-3649788