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In the paper, some classes of completely monotonic functions involving the q -gamma and q -digamma functions are derived. The monotonicity properties of these functions are exploited to establish a double inequality for the ratio of the q -gamma function and a double inequality for the q -digamma function. Moreover, a class of inequalities for the q -polygamma functions is presented. Mathematics subject classification (2010): 33D05, 26D15, 26A48.

Some classes of completely monotonic functions related to q-gamma and q-digamma functions