Log-concavity for Bernstein-type operators using stochastic orders

This paper aims to study the preservation of log-concavity for Bernstein-type operators. In particular, attention is focused on positive linear operators, defined on the positive semi-axis, admitting a probabilistic representation in terms of a process with independent increments. This class includes classical Gamma, Szász and Szász-Durrmeyer operators. As a main tool in our results we use stochastic orders techniques. Our results include, as a particular case, the log-concavity of certain functions related to the gamma incomplete function.