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In this paper we present several new classes of logarithmically completelymonotonic functions. Our functions have in common that they are defined interms of the $q-$gamma and $q-$digamma functions. As an applications of thisresults, some inequalities for the $q-$gamma and the $q-$digamma functions areestablished. Some of the given results generalized theorems due to Alzer andBerg and C.-P. Chen and F. Qi.

Logarithmically completely monotontic functions related the $q-$gamma and the $q-$digamma functions with applications