  In this paper, the logarithmically complete monotonicity property for a
functions involving $q$-gamma function is investigated for $q\in(0,1).$ As
applications of this results, some new inequalities for the $q$-gamma function
are established. Furthermore, let the sequence $r_n$ be defined by
$$n!=\sqrt{2\pi n}(n/e)^n e^{r_n}.$$ We establish new estimates for Stirling's
formula remainder $r_n.$
