Extensions of Hermite–Hadamard inequalities for harmonically convex functions via generalized fractional integrals

Xue Xiao You; Muhammad Aamir Ali; Hüseyin Budak; Praveen Agarwal; Yu Ming Chu

doi:10.1186/s13660-021-02638-3

Extensions of Hermite–Hadamard inequalities for harmonically convex functions via generalized fractional integrals

Xue Xiao You
, Muhammad Aamir Ali
, Hüseyin Budak
, Praveen Agarwal
, Yu Ming Chu

Nonlinear Dynamic Research Centre (NDRC)

Hubei Normal University
Nanjing Normal University
Duzce University
International College of Engineering
Huzhou University

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

24 Scopus citations

Abstract

In the paper, the authors establish some new Hermite–Hadamard type inequalities for harmonically convex functions via generalized fractional integrals. Moreover, the authors prove extensions of the Hermite–Hadamard inequality for harmonically convex functions via generalized fractional integrals without using the harmonic convexity property for the functions. The results offered here are the refinements of the existing results for harmonically convex functions.

Original language	English
Article number	102
Journal	Journal of Inequalities and Applications
Volume	2021
Issue number	1
DOIs	https://doi.org/10.1186/s13660-021-02638-3
State	Published - 2021

Keywords

Generalized fractional integrals
Harmonically convex functions
Hermite–Hadamard inequalities

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10.1186/s13660-021-02638-3

Cite this

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title = "Extensions of Hermite–Hadamard inequalities for harmonically convex functions via generalized fractional integrals",

abstract = "In the paper, the authors establish some new Hermite–Hadamard type inequalities for harmonically convex functions via generalized fractional integrals. Moreover, the authors prove extensions of the Hermite–Hadamard inequality for harmonically convex functions via generalized fractional integrals without using the harmonic convexity property for the functions. The results offered here are the refinements of the existing results for harmonically convex functions.",

keywords = "Generalized fractional integrals, Harmonically convex functions, Hermite–Hadamard inequalities",

author = "You, \{Xue Xiao\} and Ali, \{Muhammad Aamir\} and H{\"u}seyin Budak and Praveen Agarwal and Chu, \{Yu Ming\}",

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AU - You, Xue Xiao

AU - Ali, Muhammad Aamir

AU - Budak, Hüseyin

AU - Agarwal, Praveen

AU - Chu, Yu Ming

PY - 2021

Y1 - 2021

N2 - In the paper, the authors establish some new Hermite–Hadamard type inequalities for harmonically convex functions via generalized fractional integrals. Moreover, the authors prove extensions of the Hermite–Hadamard inequality for harmonically convex functions via generalized fractional integrals without using the harmonic convexity property for the functions. The results offered here are the refinements of the existing results for harmonically convex functions.

AB - In the paper, the authors establish some new Hermite–Hadamard type inequalities for harmonically convex functions via generalized fractional integrals. Moreover, the authors prove extensions of the Hermite–Hadamard inequality for harmonically convex functions via generalized fractional integrals without using the harmonic convexity property for the functions. The results offered here are the refinements of the existing results for harmonically convex functions.

KW - Generalized fractional integrals

KW - Harmonically convex functions

KW - Hermite–Hadamard inequalities

UR - https://www.scopus.com/pages/publications/85107539083

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DO - 10.1186/s13660-021-02638-3

M3 - Article

AN - SCOPUS:85107539083

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VL - 2021

JO - Journal of Inequalities and Applications

JF - Journal of Inequalities and Applications

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M1 - 102

ER -

Extensions of Hermite–Hadamard inequalities for harmonically convex functions via generalized fractional integrals

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Keywords

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