Products of powers of nonnegative derivatives

Abstract:

This paper contains some results concerning functions that can be written as $f_1^{{\beta _1}} \cdots f_n^{{\beta _n}}$, where $n$ is an integer greater than $1$, ${f_j}$ are nonnegative derivatives and ${\beta _j}$ are positive numbers. If we choose ${\beta _1} = \cdots = {\beta _n} = 1$, we obtain theorems about products of nonnegative derivatives.