Some inequalities bounding certain ratios of the q-gamma function

Abstract

In this short paper, we established q- analogues of some well-known inequalities for the classical Gamma function and some inequalities bounding the ratio Γ_q (x)/Γ_q (y), where Γ_q (.) is the q-analogue of the Gamma function. The method employed in presenting the results made use of strict logarithmic convexity of a function and classical mean value theorem involving the q-analogue of the psi function. At the end, the proven result provided the q-analogue of some known result concerning the classical Gamma function.