Certain midpoint-type Fejér and Hermite-Hadamard inclusions involving fractional integrals with an exponential function in kernel

Thongchai Botmart; Soubhagya Kumar Sahoo; Bibhakar Kodamasingh; Muhammad Amer Latif; Fahd Jarad; Artion Kashuri; Thongchai Botmart; Soubhagya Kumar Sahoo; Bibhakar Kodamasingh; Muhammad Amer Latif; Fahd Jarad; Artion Kashuri

doi:10.3934/math.2023283

AIMS Mathematics

2023, Volume 8, Issue 3: 5616-5638. doi: 10.3934/math.2023283

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Research article

Certain midpoint-type Fejér and Hermite-Hadamard inclusions involving fractional integrals with an exponential function in kernel

1.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
2.
Department of Mathematics, Institute of Technical Education and Research, Siksha 'O' Anusandhan University, Bhubaneswar 751030, India
3.
Department of Basic Sciences, Deanship of Preparatory Year, King Faisal University, Hofuf 31982, Al-Hasa, Saudi Arabia
4.
Department of Mathematics, Çankaya University 06790, Ankara, Turkey
5.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
6.
Department of Mathematics, Faculty of Technical and Natural Sciences, University "Ismail Qemali", 9400 Vlora, Albania
Correction on: AIMS Mathematics 8: 13785-13786.

Received: 24 October 2022 Revised: 07 December 2022 Accepted: 12 December 2022 Published: 21 December 2022
MSC : 26A51, 26A33, 26D07, 26D10, 26D15

In this paper, using positive symmetric functions, we offer two new important identities of fractional integral form for convex and harmonically convex functions. We then prove new variants of the Hermite-Hadamard-Fejér type inequalities for convex as well as harmonically convex functions via fractional integrals involving an exponential kernel. Moreover, we also present improved versions of midpoint type Hermite-Hadamard inequality. Graphical representations are given to validate the accuracy of the main results. Finally, applications associated with matrices, q-digamma functions and modifed Bessel functions are also discussed.
- Hermite-Hadamard-Fejér inequalities,
- convex function,
- harmonically convex function,
- fractional integral operators,
- matrices,
- q-digamma functions,
- modifed Bessel functions
Citation: Thongchai Botmart, Soubhagya Kumar Sahoo, Bibhakar Kodamasingh, Muhammad Amer Latif, Fahd Jarad, Artion Kashuri. Certain midpoint-type Fejér and Hermite-Hadamard inclusions involving fractional integrals with an exponential function in kernel[J]. AIMS Mathematics, 2023, 8(3): 5616-5638. doi: 10.3934/math.2023283

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Abstract

In this paper, using positive symmetric functions, we offer two new important identities of fractional integral form for convex and harmonically convex functions. We then prove new variants of the Hermite-Hadamard-Fejér type inequalities for convex as well as harmonically convex functions via fractional integrals involving an exponential kernel. Moreover, we also present improved versions of midpoint type Hermite-Hadamard inequality. Graphical representations are given to validate the accuracy of the main results. Finally, applications associated with matrices, q-digamma functions and modifed Bessel functions are also discussed.

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