Certain Hermite–Hadamard Inequalities for Logarithmically Convex Functions with Applications

By Shilpi Jain, K. Mehrez, Dumitru Băleanu, Praveen Agarwal. Mathematics, 2019

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In this paper, we discuss various estimates to the right-hand (resp. left-hand) side of the Hermite–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 q-digamma and q-polygamma functions, respectively. As a consequence, new inequalities for the q-analogue of the harmonic numbers in terms of the q-polygamma functions are derived. Moreover, several inequalities for special means are also considered.

Subfields: Applied Mathematics

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