Next Article in Journal
Optimal Derivative-Free Root Finding Methods Based on Inverse Interpolation
Next Article in Special Issue
An Efficient Numerical Technique for the Nonlinear Fractional Kolmogorov–Petrovskii–Piskunov Equation
Previous Article in Journal
The First Eigenvalue Estimates of Warped Product Pseudo-Slant Submanifolds
Previous Article in Special Issue
Global Asymptotical Stability Analysis for Fractional Neural Networks with Time-Varying Delays
Article Menu
Issue 2 (February) cover image

Export Article

Open AccessArticle
Mathematics 2019, 7(2), 163; https://doi.org/10.3390/math7020163

Certain Hermite–Hadamard Inequalities for Logarithmically Convex Functions with Applications

1
Department of Mathematics, Poornima College of Engineering, Jaipur 302022, India
2
Département de Mathématiques, Facultée des sciences de Tunis, Université Tunis El Manar, Tunis 1068, Tunisia
3
Dèpartement de Mathématiques, Issat Kasserine, Université de Kairouan, Kairouan 3100, Tunisia
4
Department of Mathematics and Computer Sciences, Faculty of Art and Sciences, Çankaya University, Balgat 0630, Turkey
5
Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India
6
Department of Mathematics, Harish-Chandra Research Institute (HRI), Allahbad 211019, India
*
Author to whom correspondence should be addressed.
Received: 12 November 2018 / Revised: 27 January 2019 / Accepted: 28 January 2019 / Published: 11 February 2019
Full-Text   |   PDF [283 KB, uploaded 22 February 2019]   |   Review Reports

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. View Full-Text
Keywords: Hermite–Hadamard inequality; log-convex function; q-digamma; q-polygamma function; harmonic number; special means Hermite–Hadamard inequality; log-convex function; q-digamma; q-polygamma function; harmonic number; special means
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Jain, S.; Mehrez, K.; Baleanu, D.; Agarwal, P. Certain Hermite–Hadamard Inequalities for Logarithmically Convex Functions with Applications. Mathematics 2019, 7, 163.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top