  This paper is inspired by the work of J. S\'{a}ndor in 2006. In the paper,
the authors establish some double inequalities involving the ratio $
\frac{\Gamma_{q}(x+1)}{ \Gamma_{q} \left( x+\frac{1}{2}\right)}$, where
$\Gamma_{q}(x)$ is the $q$-deformation of the classical Gamma function denoted
by $\Gamma(x)$. The method employed in presenting the results makes use of
Jackson's $q$-integral representation of the $q$-deformed Gamma function. In
addition, H\"{o}lder's inequality for the $q$-integral, as well as some basic
analytical techniques involving the $q$-analogue of the psi function are used.
As a consequence, $q$-analogues of the classical Wendel's asymptotic relation
are obtained. At the end, sharpness of the inequalities established in this
paper is investigated.
