Hermite-Hadamard-Fejér Inequality Related to Generalized Convex Functions via Fractional Integrals

Hermite-Hadamard-Fejér Inequality Related to Generalized Convex Functions via Fractional Integrals

This paper deals with Hermite-Hadamard-Fejér inequality for (η1,η2)-convex functions via fractional integrals. Some mid-point and trapezoid type inequalities related to Hermite-Hadamard inequality when the absolute value of derivative of considered function is (η1,η2)-convex functions are obtained....

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Main Authors: M. Rostamian Delavar, S. Mohammadi Aslani, M. De La Sen
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2018/5864091
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spelling doaj-a2d85a63c8b942fb8666b46f2a7b433b2020-11-24T21:39:28ZengHindawi LimitedJournal of Mathematics2314-46292314-47852018-01-01201810.1155/2018/58640915864091Hermite-Hadamard-Fejér Inequality Related to Generalized Convex Functions via Fractional IntegralsM. Rostamian Delavar0S. Mohammadi Aslani1M. De La Sen2Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, IranDepartment of Mathematics, Karaj Branch, Islamic Azad University, Karaj, IranInstitute of Research and Development of Processes, University of Basque Country, Campus of Leioa, Aptdo. 644, 48080 Bilbao, SpainThis paper deals with Hermite-Hadamard-Fejér inequality for (η1,η2)-convex functions via fractional integrals. Some mid-point and trapezoid type inequalities related to Hermite-Hadamard inequality when the absolute value of derivative of considered function is (η1,η2)-convex functions are obtained. Furthermore, a refinement for classic Hermite-Hadamard inequality via fractional integrals is given when a positive (η1,η2)-convex function is increasing.http://dx.doi.org/10.1155/2018/5864091
collection DOAJ
language English
format Article
sources DOAJ
author M. Rostamian Delavar
S. Mohammadi Aslani
M. De La Sen
spellingShingle M. Rostamian Delavar
S. Mohammadi Aslani
M. De La Sen
Hermite-Hadamard-Fejér Inequality Related to Generalized Convex Functions via Fractional Integrals
Journal of Mathematics
author_facet M. Rostamian Delavar
S. Mohammadi Aslani
M. De La Sen
author_sort M. Rostamian Delavar
title Hermite-Hadamard-Fejér Inequality Related to Generalized Convex Functions via Fractional Integrals
title_short Hermite-Hadamard-Fejér Inequality Related to Generalized Convex Functions via Fractional Integrals
title_full Hermite-Hadamard-Fejér Inequality Related to Generalized Convex Functions via Fractional Integrals
title_fullStr Hermite-Hadamard-Fejér Inequality Related to Generalized Convex Functions via Fractional Integrals
title_full_unstemmed Hermite-Hadamard-Fejér Inequality Related to Generalized Convex Functions via Fractional Integrals
title_sort hermite-hadamard-fejér inequality related to generalized convex functions via fractional integrals
publisher Hindawi Limited
series Journal of Mathematics
issn 2314-4629
2314-4785
publishDate 2018-01-01
description This paper deals with Hermite-Hadamard-Fejér inequality for (η1,η2)-convex functions via fractional integrals. Some mid-point and trapezoid type inequalities related to Hermite-Hadamard inequality when the absolute value of derivative of considered function is (η1,η2)-convex functions are obtained. Furthermore, a refinement for classic Hermite-Hadamard inequality via fractional integrals is given when a positive (η1,η2)-convex function is increasing.
url http://dx.doi.org/10.1155/2018/5864091
work_keys_str_mv AT mrostamiandelavar hermitehadamardfejerinequalityrelatedtogeneralizedconvexfunctionsviafractionalintegrals
AT smohammadiaslani hermitehadamardfejerinequalityrelatedtogeneralizedconvexfunctionsviafractionalintegrals
AT mdelasen hermitehadamardfejerinequalityrelatedtogeneralizedconvexfunctionsviafractionalintegrals
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