A criterion for the contiguity of quasiconcave functions (Q1810008)

As is known, a function \(\varphi(t)\) on the semi-infinite interval \([0,\infty)\) is said to be quasiconcave if \(\varphi(0)= 0\), \(\varphi(t)\) is positive and increases for \(t> 0\), and the function \(\varphi(t)/t\) decreases for \(t> 0\). Using linear-constant step-functions, the authors find a new description of the classification of quasiconcave functions. This criterion is obtained in terms of nodes of the corresponding linear-constant step-functions. It turns out that nodes must be equivalent to sequences.