New Hermite–Hadamard type integral inequalities for convex functions and their applications

Khaled Mehrez; Praveen Agarwal

doi:10.1016/j.cam.2018.10.022

New Hermite–Hadamard type integral inequalities for convex functions and their applications

Khaled Mehrez
, Praveen Agarwal

Université de Tunis El Manar
University of Kairouan
International College of Engineering

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

113 Scopus citations

Abstract

In this paper, we establish (presumably new type) integral inequalities for convex functions via the Hermite–Hadamard's inequalities. As applications, we apply these new inequalities to construct inequalities involving special means of real numbers, some error estimates for the formula midpoint are given. Finally, new inequalities for some special and [Formula presented]-special functions are also pointed out.

Original language	English
Pages (from-to)	274-285
Number of pages	12
Journal	Journal of Computational and Applied Mathematics
Volume	350
DOIs	https://doi.org/10.1016/j.cam.2018.10.022
State	Published - Apr 2019
Externally published	Yes

Keywords

Convex functions
Hermite–Hadamard inequality
Midpoint formula
Modified Bessel function
Special means
[Formula presented]-digamma function

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10.1016/j.cam.2018.10.022

Cite this

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title = "New Hermite–Hadamard type integral inequalities for convex functions and their applications",

abstract = "In this paper, we establish (presumably new type) integral inequalities for convex functions via the Hermite–Hadamard's inequalities. As applications, we apply these new inequalities to construct inequalities involving special means of real numbers, some error estimates for the formula midpoint are given. Finally, new inequalities for some special and [Formula presented]-special functions are also pointed out.",

keywords = "Convex functions, Hermite–Hadamard inequality, Midpoint formula, Modified Bessel function, Special means, [Formula presented]-digamma function",

author = "Khaled Mehrez and Praveen Agarwal",

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AU - Mehrez, Khaled

AU - Agarwal, Praveen

PY - 2019/4

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N2 - In this paper, we establish (presumably new type) integral inequalities for convex functions via the Hermite–Hadamard's inequalities. As applications, we apply these new inequalities to construct inequalities involving special means of real numbers, some error estimates for the formula midpoint are given. Finally, new inequalities for some special and [Formula presented]-special functions are also pointed out.

AB - In this paper, we establish (presumably new type) integral inequalities for convex functions via the Hermite–Hadamard's inequalities. As applications, we apply these new inequalities to construct inequalities involving special means of real numbers, some error estimates for the formula midpoint are given. Finally, new inequalities for some special and [Formula presented]-special functions are also pointed out.

KW - Convex functions

KW - Hermite–Hadamard inequality

KW - Midpoint formula

KW - Modified Bessel function

KW - Special means

KW - [Formula presented]-digamma function

UR - https://www.scopus.com/pages/publications/85056201798

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DO - 10.1016/j.cam.2018.10.022

M3 - Article

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SN - 0377-0427

VL - 350

SP - 274

EP - 285

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

ER -

New Hermite–Hadamard type integral inequalities for convex functions and their applications

Abstract

Keywords

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