Some operations preserving log-concavity of nonnegative functions

In this paper we introduce the notions of k -log-concave and k, [p, q] -concave functions, as generalizations of log-concave and concave sequences, respectively. We also present sufficient conditions under which some operations with such functions yield k -log-concave functions. In particular, we infer that the convolution of a positive 1 -log-concave sequence and a nonnegative sequence of k + 1 elements is k -log-concave.