Certain midpoint-type Fejér and Hermite-Hadamard inclusions involving fractional integrals with an exponential function in kernel-Reference-Cited by-同舟云学术

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

Published:2022 Issue:3 Volume:8 Page:5616-5638
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Botmart Thongchai¹,Sahoo Soubhagya Kumar²,Kodamasingh Bibhakar²,Latif Muhammad Amer³,Jarad Fahd⁴⁵,Kashuri Artion⁶

Affiliation:

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

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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