COMMENTS ON TWO COMPLETELY MONOTONIC FUNCTIONS INVOLVING THE q-TRIGAMMA FUNCTION

In the papers [F. Qi, A completely monotonic function related to the q-trigamma function, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 7 6 (2014), no. 1, 107{114] and [J.-L. Zhao, A completely monotonic function relating to the q-trigamma function,J. Math. Inequal. 9 (2015), no. 1, 53{60; Available online at http ://dx.do i.org/10.7153/jmi-09-05], Qi and Zhao proved the complete monotonicity of two functions involving the q-trigamma function. These two functions originate and generalize the same function involving the classical trigamma function. In current paper, the authors compare with and comments on these two functions and related results obtained in the above-mentioned two papers. Moreover, the authors correct some errors by repeating the proof supplied by Qi in the above-mentioned paper published in 2014.