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: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2018/5864091 |
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| _version_ | 1832556206637449216 |
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| author | M. Rostamian Delavar S. Mohammadi Aslani M. De La Sen |
| author_facet | M. Rostamian Delavar S. Mohammadi Aslani M. De La Sen |
| author_sort | M. Rostamian Delavar |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-a2d85a63c8b942fb8666b46f2a7b433b |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-a2d85a63c8b942fb8666b46f2a7b433b2025-02-03T05:46:09ZengWileyJournal 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 |
| 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 |
| title | 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_short | Hermite-Hadamard-Fejér Inequality Related to Generalized Convex Functions via Fractional Integrals |
| title_sort | hermite hadamard fejer inequality related to generalized convex functions via fractional integrals |
| url | http://dx.doi.org/10.1155/2018/5864091 |
| work_keys_str_mv | AT mrostamiandelavar hermitehadamardfejerinequalityrelatedtogeneralizedconvexfunctionsviafractionalintegrals AT smohammadiaslani hermitehadamardfejerinequalityrelatedtogeneralizedconvexfunctionsviafractionalintegrals AT mdelasen hermitehadamardfejerinequalityrelatedtogeneralizedconvexfunctionsviafractionalintegrals |