  We consider convexity and monotonicity properties for some functions related
to the $q$-gamma function. As applications, we give a variety of inequalities
for the $q$-gamma function, the $q$-digamma function $\psi_q(x)$, and the
$q$-series. Among other consequences, we improve a result of
Azler~and~Grinshpan about the zeros of the function $\psi_q(x)$.
  We use $q$-analogues for the Gauss multiplication formula to put in closed
form members of some of our inequalities.
