Weighted midpoint hermite-hadamard-fejér type inequalities in fractional calculus for harmonically convex functions

Humaira Kalsoom; Miguel Vivas-Cortez; Muhammad Amer Latif; Hijaz Ahmad

doi:10.3390/fractalfract5040252

Weighted midpoint hermite-hadamard-fejér type inequalities in fractional calculus for harmonically convex functions

Humaira Kalsoom
, Miguel Vivas-Cortez^*
, Muhammad Amer Latif^*
, Hijaz Ahmad

^*Corresponding author for this work

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

20 Scopus citations

Abstract

In this paper, we establish a new version of Hermite-Hadamard-Fejér type inequality for harmonically convex functions in the form of weighted fractional integral. Secondly, an integral identity and some weighted midpoint fractional Hermite-Hadamard-Fejér type integral inequalities for harmonically convex functions by involving a positive weighted symmetric functions have been obtained. As shown, all of the resulting inequalities generalize several well-known inequalities, including classical and Riemann–Liouville fractional integral inequalities.

Original language	English
Article number	252
Journal	Fractal and Fractional
Volume	5
Issue number	4
DOIs	https://doi.org/10.3390/fractalfract5040252
State	Published - 2 Dec 2021
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.

Funding

Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China.

Funders	Funder number
Zhejiang Normal University	321004

Keywords

Harmonically convex functions
Hermite-Hadamard-Fejér type inequality
Symmetry
Weighted fractional operators

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10.3390/fractalfract5040252

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title = "Weighted midpoint hermite-hadamard-fej{\'e}r type inequalities in fractional calculus for harmonically convex functions",

abstract = "In this paper, we establish a new version of Hermite-Hadamard-Fej{\'e}r type inequality for harmonically convex functions in the form of weighted fractional integral. Secondly, an integral identity and some weighted midpoint fractional Hermite-Hadamard-Fej{\'e}r type integral inequalities for harmonically convex functions by involving a positive weighted symmetric functions have been obtained. As shown, all of the resulting inequalities generalize several well-known inequalities, including classical and Riemann–Liouville fractional integral inequalities.",

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AU - Kalsoom, Humaira

AU - Vivas-Cortez, Miguel

AU - Latif, Muhammad Amer

AU - Ahmad, Hijaz

PY - 2021/12/2

Y1 - 2021/12/2

N2 - In this paper, we establish a new version of Hermite-Hadamard-Fejér type inequality for harmonically convex functions in the form of weighted fractional integral. Secondly, an integral identity and some weighted midpoint fractional Hermite-Hadamard-Fejér type integral inequalities for harmonically convex functions by involving a positive weighted symmetric functions have been obtained. As shown, all of the resulting inequalities generalize several well-known inequalities, including classical and Riemann–Liouville fractional integral inequalities.

AB - In this paper, we establish a new version of Hermite-Hadamard-Fejér type inequality for harmonically convex functions in the form of weighted fractional integral. Secondly, an integral identity and some weighted midpoint fractional Hermite-Hadamard-Fejér type integral inequalities for harmonically convex functions by involving a positive weighted symmetric functions have been obtained. As shown, all of the resulting inequalities generalize several well-known inequalities, including classical and Riemann–Liouville fractional integral inequalities.

KW - Harmonically convex functions

KW - Hermite-Hadamard-Fejér type inequality

KW - Symmetry

KW - Weighted fractional operators

UR - https://www.scopus.com/pages/publications/85121298449

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DO - 10.3390/fractalfract5040252

M3 - Article

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JO - Fractal and Fractional

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IS - 4

M1 - 252

ER -

Weighted midpoint hermite-hadamard-fejér type inequalities in fractional calculus for harmonically convex functions

Abstract

Bibliographical note

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Keywords

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