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

Muhammad Amer Latif; Humaira Kalsoom; Zareen A. Khan; Muhammad Amer Latif; Humaira Kalsoom; Zareen A. Khan

doi:10.3934/math.2022232

AIMS Mathematics

2022, Volume 7, Issue 3: 4176-4198. doi: 10.3934/math.2022232

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Research article

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

1.
Department of Basic Sciences, Deanship of Preparatory Year, King Faisal University, Hofuf 31982, Al-Hasa, Saudi Arabia
2.
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
3.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P. O. Box 84428, Riyadh 11671, Saudi Arabia

Received: 13 October 2021 Revised: 21 November 2021 Accepted: 24 November 2021 Published: 17 December 2021
MSC : 26A51, 26A33, 26D07, 26D10, 26D15

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.
- harmonically symmetric function,
- weighted fractional operators,
- harmonic convex functions,
- Hermite-Hadamard-Fejér inequality
Citation: Muhammad Amer Latif, Humaira Kalsoom, Zareen A. Khan. Hermite-Hadamard-Fejér type fractional inequalities relating to a convex harmonic function and a positive symmetric increasing function[J]. AIMS Mathematics, 2022, 7(3): 4176-4198. doi: 10.3934/math.2022232

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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.

References

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