TWO MONOTONIC FUNCTIONS DEFINED BY TWO DERIVATIVES OF A FUNCTION INVOLVING TRIGAMMA FUNCTIONFENG QI (pp. 91-104)
Abstract. In the paper, by virtue of the convolution theorem for the Laplace transforms, with the help of monotonicity and logarithmic concavity of a function involving exponential function, and by means of analytic techniques, the author presents necessary and sufficient conditions for two functions defined by two derivatives of a function involving trigamma function to be completely monotonic or monotonic.
Keywords:complete monotonicity, monotonicity, necessary and sufficient condition, trigamma function, derivative, convolution theorem, Laplace transforms, exponential function, logarithmic concavity, inequality.