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Mathematics 2018, 6(7), 122; https://doi.org/10.3390/math6070122

A Generalized Fejér–Hadamard Inequality for Harmonically Convex Functions via Generalized Fractional Integral Operator and Related Results

1
Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University, Jinju 52828, Korea
2
Center for General Education, China Medical University, Taichung 40402, Taiwan
3
Department of Mathematics, Government College Bhalwal, Sargodha 40100, Pakistan
4
Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
5
Department of Mathematics, COMSATS University Islamabad, Attock Campus 43600, Pakistan
6
Division of Science and Technology, University of Education, Lahore 54000, Pakistan
*
Author to whom correspondence should be addressed.
Received: 5 June 2018 / Revised: 7 July 2018 / Accepted: 9 July 2018 / Published: 11 July 2018
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Abstract

In this paper, we obtain a version of the Fejér–Hadamard inequality for harmonically convex functions via generalized fractional integral operator. In addition, we establish an integral identity and some Fejér–Hadamard type integral inequalities for harmonically convex functions via a generalized fractional integral operator. Being generalizations, our results reproduce some known results. View Full-Text
Keywords: harmonically convex functions; Hermite–Hadamard inequality; generalized fractional integral operator; Mittag–Leffler function harmonically convex functions; Hermite–Hadamard inequality; generalized fractional integral operator; Mittag–Leffler function
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Kang, S.M.; Abbas, G.; Farid, G.; Nazeer, W. A Generalized Fejér–Hadamard Inequality for Harmonically Convex Functions via Generalized Fractional Integral Operator and Related Results. Mathematics 2018, 6, 122.

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