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Research Article | Open Access

Hermite-Hadamard-Fejér type fractional inequalities relating to a convex harmonic function and a positive symmetric increasing function

Muhammad Amer Latif1Humaira Kalsoom2( )Zareen A. Khan3( )
Department of Basic Sciences, Deanship of Preparatory Year, King Faisal University, Hofuf 31982, Al-Hasa, Saudi Arabia
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P. O. Box 84428, Riyadh 11671, Saudi Arabia
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Abstract

The purpose of this article is to discuss some midpoint type HHF fractional integral inequalities and related results for a class of fractional operators (weighted fractional operators) that refer to harmonic convex functions with respect to an increasing function that contains a positive weighted symmetric function with respect to the harmonic mean of the endpoints of the interval. It can be concluded from all derived inequalities that our study generalizes a large number of well-known inequalities involving both classical and Riemann-Liouville fractional integral inequalities.

CLC number: 26A51, 26A33, 26D07, 26D10, 26D15

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AIMS Mathematics
Pages 4176-4198

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Cite this article:
Latif MA, Kalsoom H, Khan ZA. Hermite-Hadamard-Fejér type fractional inequalities relating to a convex harmonic function and a positive symmetric increasing function. AIMS Mathematics, 2022, 7(3): 4176-4198. https://doi.org/10.3934/math.2022232

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Received: 13 October 2021
Revised: 21 November 2021
Accepted: 24 November 2021
Published: 15 March 2021
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)