Certain Hermite–Hadamard Inequalities for Logarithmically Convex Functions with Applications

Shilpi Jain, Khaled Mehrez, Dumitru Baleanu and Praveen Agarwal
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Shilpi Jain: Department of Mathematics, Poornima College of Engineering, Jaipur 302022, India
Khaled Mehrez: Département de Mathématiques, Facultée des sciences de Tunis, Université Tunis El Manar, Tunis 1068, Tunisia
Dumitru Baleanu: Department of Mathematics and Computer Sciences, Faculty of Art and Sciences, Çankaya University, Balgat 0630, Turkey
Praveen Agarwal: Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India

Mathematics, 2019, vol. 7, issue 2, 1-12

Abstract: 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.

Keywords: Hermite–Hadamard inequality; log-convex function; q-digamma; q-polygamma function; harmonic number; special means (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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