Certain hermite-hadamard inequalities for logarithmically convex functions with applications

Shilpi Jain; Khaled Mehrez; Dumitru Baleanu; Praveen Agarwal

doi:10.3390/math7020163

Certain hermite-hadamard inequalities for logarithmically convex functions with applications

Shilpi Jain
, Khaled Mehrez
, Dumitru Baleanu
, Praveen Agarwal

Poornima College of Engineering
Université de Tunis El Manar
University of Kairouan
Cankaya University
International College of Engineering
Harish Chandra Research Institute

Research output: Contribution to journal › Article › peer-review

63 Scopus citations

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.

Original language	English
Article number	163
Journal	Mathematics
Volume	7
Issue number	2
DOIs	https://doi.org/10.3390/math7020163
State	Published - 11 Feb 2019
Externally published	Yes

Keywords

Harmonic number
Hermite-Hadamard inequality
Log-convex function
Q-digamma
Q-polygamma function
Special means

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10.3390/math7020163

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title = "Certain hermite-hadamard inequalities for logarithmically convex functions with applications",

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 = "Harmonic number, Hermite-Hadamard inequality, Log-convex function, Q-digamma, Q-polygamma function, Special means",

author = "Shilpi Jain and Khaled Mehrez and Dumitru Baleanu and Praveen Agarwal",

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AU - Jain, Shilpi

AU - Mehrez, Khaled

AU - Baleanu, Dumitru

AU - Agarwal, Praveen

PY - 2019/2/11

Y1 - 2019/2/11

N2 - 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.

AB - 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.

KW - Harmonic number

KW - Hermite-Hadamard inequality

KW - Log-convex function

KW - Q-digamma

KW - Q-polygamma function

KW - Special means

UR - https://www.scopus.com/pages/publications/85061355026

U2 - 10.3390/math7020163

DO - 10.3390/math7020163

M3 - Article

AN - SCOPUS:85061355026

SN - 2227-7390

VL - 7

JO - Mathematics

JF - Mathematics

IS - 2

M1 - 163

ER -

Certain hermite-hadamard inequalities for logarithmically convex functions with applications

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Keywords

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