Hadamard Inequalities for Strongly α,m-Convex Functions via Caputo Fractional Derivatives
In this paper, we present two versions of the Hadamard inequality for α,m convex functions via Caputo fractional derivatives. Several related results are analyzed for convex and m-convex functions along with their refinements and generalizations. The error bounds of the Hadamard inequalities are est...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6691151 |
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| _version_ | 1832546828609912832 |
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| author | Yanliang Dong Muhammad Zeb Ghulam Farid Sidra Bibi |
| author_facet | Yanliang Dong Muhammad Zeb Ghulam Farid Sidra Bibi |
| author_sort | Yanliang Dong |
| collection | DOAJ |
| description | In this paper, we present two versions of the Hadamard inequality for α,m convex functions via Caputo fractional derivatives. Several related results are analyzed for convex and m-convex functions along with their refinements and generalizations. The error bounds of the Hadamard inequalities are established by applying some known identities. |
| format | Article |
| id | doaj-art-ad3f07724eb44fd0bbf1338436fde536 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-ad3f07724eb44fd0bbf1338436fde5362025-02-03T06:47:03ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/66911516691151Hadamard Inequalities for Strongly α,m-Convex Functions via Caputo Fractional DerivativesYanliang Dong0Muhammad Zeb1Ghulam Farid2Sidra Bibi3Mechanical and Electrical Engineering College, Rizhao Polytechnic, Rizhao City 276826, Shandong, ChinaDepartment of Mathematics, COMSATS University Islamabad, Islamabad, Attock Campus, PakistanDepartment of Mathematics, COMSATS University Islamabad, Islamabad, Attock Campus, PakistanGovernment Girls Primary School, Kamra Khurd, Attock 43570, PakistanIn this paper, we present two versions of the Hadamard inequality for α,m convex functions via Caputo fractional derivatives. Several related results are analyzed for convex and m-convex functions along with their refinements and generalizations. The error bounds of the Hadamard inequalities are established by applying some known identities.http://dx.doi.org/10.1155/2021/6691151 |
| spellingShingle | Yanliang Dong Muhammad Zeb Ghulam Farid Sidra Bibi Hadamard Inequalities for Strongly α,m-Convex Functions via Caputo Fractional Derivatives Journal of Mathematics |
| title | Hadamard Inequalities for Strongly α,m-Convex Functions via Caputo Fractional Derivatives |
| title_full | Hadamard Inequalities for Strongly α,m-Convex Functions via Caputo Fractional Derivatives |
| title_fullStr | Hadamard Inequalities for Strongly α,m-Convex Functions via Caputo Fractional Derivatives |
| title_full_unstemmed | Hadamard Inequalities for Strongly α,m-Convex Functions via Caputo Fractional Derivatives |
| title_short | Hadamard Inequalities for Strongly α,m-Convex Functions via Caputo Fractional Derivatives |
| title_sort | hadamard inequalities for strongly α m convex functions via caputo fractional derivatives |
| url | http://dx.doi.org/10.1155/2021/6691151 |
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