Hermite–Hadamard-type inequalities for functions whose derivatives are η-convex via fractional integrals

Hermite–Hadamard-type inequalities for functions whose derivatives are η-convex via fractional integrals

Abstract In the present research, we develop some integral inequalities of Hermite–Hadamard type for differentiable η-convex functions. Moreover, our results include several new and known results as particular cases.

Bibliographic Details
Main Authors: Young Chel Kwun, Muhammad Shoaib Saleem, Mamoona Ghafoor, Waqas Nazeer, Shin Min Kang
Format: Article
Language:English
Published: SpringerOpen 2019-02-01
Series:Journal of Inequalities and Applications
Subjects:
Convex function
η-convex function
Hermite–Hadamard-type inequality
Fractional integral
Online Access:http://link.springer.com/article/10.1186/s13660-019-1993-y
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spelling doaj-354dde2fe4924000b4f3c63589dddddd2020-11-25T01:10:22ZengSpringerOpenJournal of Inequalities and Applications1029-242X2019-02-012019111610.1186/s13660-019-1993-yHermite–Hadamard-type inequalities for functions whose derivatives are η-convex via fractional integralsYoung Chel Kwun0Muhammad Shoaib Saleem1Mamoona Ghafoor2Waqas Nazeer3Shin Min Kang4Department of Mathematics, Dong-A UniversityDepartment of Mathematics, University of OkaraDepartment of Mathematics, University of OkaraDivision of Science and Technology, University of EducationDepartment of Mathematics and Research Institute of Natural Science, Gyeongsang National UniversityAbstract In the present research, we develop some integral inequalities of Hermite–Hadamard type for differentiable η-convex functions. Moreover, our results include several new and known results as particular cases.http://link.springer.com/article/10.1186/s13660-019-1993-yConvex functionη-convex functionHermite–Hadamard-type inequalityFractional integral
collection DOAJ
language English
format Article
sources DOAJ
author Young Chel Kwun
Muhammad Shoaib Saleem
Mamoona Ghafoor
Waqas Nazeer
Shin Min Kang
spellingShingle Young Chel Kwun
Muhammad Shoaib Saleem
Mamoona Ghafoor
Waqas Nazeer
Shin Min Kang
Hermite–Hadamard-type inequalities for functions whose derivatives are η-convex via fractional integrals
Journal of Inequalities and Applications
Convex function
η-convex function
Hermite–Hadamard-type inequality
Fractional integral
author_facet Young Chel Kwun
Muhammad Shoaib Saleem
Mamoona Ghafoor
Waqas Nazeer
Shin Min Kang
author_sort Young Chel Kwun
title Hermite–Hadamard-type inequalities for functions whose derivatives are η-convex via fractional integrals
title_short Hermite–Hadamard-type inequalities for functions whose derivatives are η-convex via fractional integrals
title_full Hermite–Hadamard-type inequalities for functions whose derivatives are η-convex via fractional integrals
title_fullStr Hermite–Hadamard-type inequalities for functions whose derivatives are η-convex via fractional integrals
title_full_unstemmed Hermite–Hadamard-type inequalities for functions whose derivatives are η-convex via fractional integrals
title_sort hermite–hadamard-type inequalities for functions whose derivatives are η-convex via fractional integrals
publisher SpringerOpen
series Journal of Inequalities and Applications
issn 1029-242X
publishDate 2019-02-01
description Abstract In the present research, we develop some integral inequalities of Hermite–Hadamard type for differentiable η-convex functions. Moreover, our results include several new and known results as particular cases.
topic Convex function
η-convex function
Hermite–Hadamard-type inequality
Fractional integral
url http://link.springer.com/article/10.1186/s13660-019-1993-y
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AT muhammadshoaibsaleem hermitehadamardtypeinequalitiesforfunctionswhosederivativesareēconvexviafractionalintegrals
AT mamoonaghafoor hermitehadamardtypeinequalitiesforfunctionswhosederivativesareēconvexviafractionalintegrals
AT waqasnazeer hermitehadamardtypeinequalitiesforfunctionswhosederivativesareēconvexviafractionalintegrals
AT shinminkang hermitehadamardtypeinequalitiesforfunctionswhosederivativesareēconvexviafractionalintegrals
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