摘要 : Our main goal in this paper is to introduce new classes of logarithmically completely monotonic functions involving q-gamma function. As applications, new classes of Bernstein functions related to the q-gamma function and dilogari... 展开 Our main goal in this paper is to introduce new classes of logarithmically completely monotonic functions involving q-gamma function. As applications, new classes of Bernstein functions related to the q-gamma function and dilogarithm are established with its integral representation. Moreover, various new sharp bounds for the q-digamma and q-trigamma functions are derived. In particular, sharp bounds for the q-analogue of harmonic numbers are established as a consequence. The results obtained in this work are new. The limiting case q -> 1, in the results obtained in this paper leads to the results for a class of Bernstein functions and logarithmically completely monotonic function involving Euler's gamma function and dilogarithm, which are also new in the literature. 收起