Monotonic functions related to the q-gamma function

Abstract

In this paper, the monotonicity property for two functions involving the logarithmic of the q-gamma function is proven for all \(q>0\). As a consequence, sharp inequalities for the q-gamma function are established. Our results are shown to be as a generalization of results which were obtained by Anderson and Qiu (Proc Am Math Soc 125:3355–3362, 1997).