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

Shin Min Kang, Ghulam Abbas, Ghulam Farid and Waqas Nazeer
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Shin Min Kang: Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University, Jinju 52828, Korea
Ghulam Abbas: Department of Mathematics, Government College Bhalwal, Sargodha 40100, Pakistan
Ghulam Farid: Department of Mathematics, COMSATS University Islamabad, Attock Campus 43600, Pakistan
Waqas Nazeer: Division of Science and Technology, University of Education, Lahore 54000, Pakistan

Mathematics, 2018, vol. 6, issue 7, 1-16

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.

Keywords: harmonically convex functions; Hermite–Hadamard inequality; generalized fractional integral operator; Mittag–Leffler function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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