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

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

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 harmonic...

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Main Authors: Shin Min Kang, Ghulam Abbas, Ghulam Farid, Waqas Nazeer
Format: Article
Language:English
Published: MDPI AG 2018-07-01
Series:Mathematics
Subjects:
harmonically convex functions
Hermite–Hadamard inequality
generalized fractional integral operator
Mittag–Leffler function
Online Access:http://www.mdpi.com/2227-7390/6/7/122
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spelling doaj-21c44b3761f74a2888e7a43e07a3020b2020-11-25T02:32:53ZengMDPI AGMathematics2227-73902018-07-016712210.3390/math6070122math6070122A Generalized Fejér–Hadamard Inequality for Harmonically Convex Functions via Generalized Fractional Integral Operator and Related ResultsShin Min Kang0Ghulam Abbas1Ghulam Farid2Waqas Nazeer3Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University, Jinju 52828, KoreaDepartment of Mathematics, Government College Bhalwal, Sargodha 40100, PakistanDepartment of Mathematics, COMSATS University Islamabad, Attock Campus 43600, PakistanDivision of Science and Technology, University of Education, Lahore 54000, PakistanIn 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.http://www.mdpi.com/2227-7390/6/7/122harmonically convex functionsHermite–Hadamard inequalitygeneralized fractional integral operatorMittag–Leffler function
collection DOAJ
language English
format Article
sources DOAJ
author Shin Min Kang
Ghulam Abbas
Ghulam Farid
Waqas Nazeer
spellingShingle Shin Min Kang
Ghulam Abbas
Ghulam Farid
Waqas Nazeer
A Generalized Fejér–Hadamard Inequality for Harmonically Convex Functions via Generalized Fractional Integral Operator and Related Results
Mathematics
harmonically convex functions
Hermite–Hadamard inequality
generalized fractional integral operator
Mittag–Leffler function
author_facet Shin Min Kang
Ghulam Abbas
Ghulam Farid
Waqas Nazeer
author_sort Shin Min Kang
title A Generalized Fejér–Hadamard Inequality for Harmonically Convex Functions via Generalized Fractional Integral Operator and Related Results
title_short A Generalized Fejér–Hadamard Inequality for Harmonically Convex Functions via Generalized Fractional Integral Operator and Related Results
title_full A Generalized Fejér–Hadamard Inequality for Harmonically Convex Functions via Generalized Fractional Integral Operator and Related Results
title_fullStr A Generalized Fejér–Hadamard Inequality for Harmonically Convex Functions via Generalized Fractional Integral Operator and Related Results
title_full_unstemmed A Generalized Fejér–Hadamard Inequality for Harmonically Convex Functions via Generalized Fractional Integral Operator and Related Results
title_sort generalized fejér–hadamard inequality for harmonically convex functions via generalized fractional integral operator and related results
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2018-07-01
description 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.
topic harmonically convex functions
Hermite–Hadamard inequality
generalized fractional integral operator
Mittag–Leffler function
url http://www.mdpi.com/2227-7390/6/7/122
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AT ghulamabbas ageneralizedfejerhadamardinequalityforharmonicallyconvexfunctionsviageneralizedfractionalintegraloperatorandrelatedresults
AT ghulamfarid ageneralizedfejerhadamardinequalityforharmonicallyconvexfunctionsviageneralizedfractionalintegraloperatorandrelatedresults
AT waqasnazeer ageneralizedfejerhadamardinequalityforharmonicallyconvexfunctionsviageneralizedfractionalintegraloperatorandrelatedresults
AT shinminkang generalizedfejerhadamardinequalityforharmonicallyconvexfunctionsviageneralizedfractionalintegraloperatorandrelatedresults
AT ghulamabbas generalizedfejerhadamardinequalityforharmonicallyconvexfunctionsviageneralizedfractionalintegraloperatorandrelatedresults
AT ghulamfarid generalizedfejerhadamardinequalityforharmonicallyconvexfunctionsviageneralizedfractionalintegraloperatorandrelatedresults
AT waqasnazeer generalizedfejerhadamardinequalityforharmonicallyconvexfunctionsviageneralizedfractionalintegraloperatorandrelatedresults
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