Completely monotonic functions related to the q-gamma and the q-trigamma functions

In this paper, two completely monotonic functions involving the q-gamma and the q-trigamma functions where q is a positive real, are introduced and exploited to derive sharp bounds for the q-gamma function in terms of the q-trigamma function. These results, when letting q → 1, are shown to be new. Also, sharp bounds for the q-digamma function in terms of the q-tetragamma function are derived. Furthermore, an infinite class of inequalities for the q-polygamma function is established.