Midpoint inequalities in fractional calculus defined using positive weighted symmetry function kernels

Pshtiwan Othman Mohammed; Hassen Aydi; Artion Kashuri; Y. S. Hamed; Khadijah M. Abualnaja

doi:10.3390/sym13040550

Midpoint inequalities in fractional calculus defined using positive weighted symmetry function kernels

Pshtiwan Othman Mohammed^*, Hassen Aydi^*, Artion Kashuri, Y. S. Hamed, Khadijah M. Abualnaja

^*Corresponding author for this work

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

35 Citations (Scopus)

Abstract

The aim of our study is to establish, for convex functions on an interval, a midpoint version of the fractional HHF type inequality. The corresponding fractional integral has a symmetric weight function composed with an increasing function as integral kernel. We also consider a midpoint identity and establish some related inequalities based on this identity. Some special cases can be considered from our main results. These results confirm the generality of our attempt.

Original language	English
Article number	550
Journal	Symmetry
Volume	13
Issue number	4
DOIs	https://doi.org/10.3390/sym13040550
Publication status	Published - Apr 2021
Externally published	Yes

Keywords

Convex functions
HHF type inequality
Symmetry
Weighted fractional operators

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10.3390/sym13040550

Cite this

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abstract = "The aim of our study is to establish, for convex functions on an interval, a midpoint version of the fractional HHF type inequality. The corresponding fractional integral has a symmetric weight function composed with an increasing function as integral kernel. We also consider a midpoint identity and establish some related inequalities based on this identity. Some special cases can be considered from our main results. These results confirm the generality of our attempt.",

keywords = "Convex functions, HHF type inequality, Symmetry, Weighted fractional operators",

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AU - Hamed, Y. S.

AU - Abualnaja, Khadijah M.

PY - 2021/4

Y1 - 2021/4

N2 - The aim of our study is to establish, for convex functions on an interval, a midpoint version of the fractional HHF type inequality. The corresponding fractional integral has a symmetric weight function composed with an increasing function as integral kernel. We also consider a midpoint identity and establish some related inequalities based on this identity. Some special cases can be considered from our main results. These results confirm the generality of our attempt.

AB - The aim of our study is to establish, for convex functions on an interval, a midpoint version of the fractional HHF type inequality. The corresponding fractional integral has a symmetric weight function composed with an increasing function as integral kernel. We also consider a midpoint identity and establish some related inequalities based on this identity. Some special cases can be considered from our main results. These results confirm the generality of our attempt.

KW - Convex functions

KW - HHF type inequality

KW - Symmetry

KW - Weighted fractional operators

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Midpoint inequalities in fractional calculus defined using positive weighted symmetry function kernels

Abstract

Keywords

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