A $ q$-analogue of complete monotonicity
The aim of this paper is to give a $q$-analogue for complete monotonicity. We apply a classical characterization of Hausdorff moment sequences in terms of positive definiteness and complete monotonicity, adapted to the $q$-situation. The method due to Maserick and Szafraniec that does not need moments turns out to be useful. A definition of a $q$-moment sequence appears as a by-product.