Mehrez, KhaledBaleanu, DumitruAgarwal, PraveenJain, Shilpi2020-01-152025-09-182020-01-152025-09-182019Jain, Shilpi...et al. (2019). "Certain Hermite-Hadamard Inequalities for Logarithmically Convex Functions with Applications", Mathematics, Vol. 7, No. 2.2227-7390https://doi.org/10.3390/math7020163https://hdl.handle.net/20.500.12416/12163Mehrez, Khaled/0000-0001-9948-3636; Agarwal, Praveen/0000-0001-7556-8942; Jain, Shilpi/0000-0002-0906-2801In 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.eninfo:eu-repo/semantics/openAccessHermite-Hadamard InequalityLog-Convex FunctionQ-DigammaQ-Polygamma FunctionHarmonic NumberSpecial MeansArticle10.3390/math70201632-s2.0-85061355026