Certain Hermite–Hadamard Inequalities for Logarithmically Convex Functions with Applications

In this paper, we discuss various estimates to the right-hand (resp. left-hand) side of the Hermite&#8315;Hadamard inequality for functions whose absolute values of the second (resp. first) derivatives to positive real powers are log-convex. As an application, we derive certain inequalities involving the <i>q</i>-digamma and <i>q</i>-polygamma functions, respectively. As a consequence, new inequalities for the <i>q</i>-analogue of the harmonic numbers in terms of the <i>q</i>-polygamma functions are derived. Moreover, several inequalities for special means are also considered.

Abstract licence: CC BY

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