Caputo Fractional Derivative Hadamard Inequalities for Strongly m-Convex Functions
In this paper, two versions of the Hadamard inequality are obtained by using Caputo fractional derivatives and strongly m-convex functions. The established results will provide refinements of well-known Caputo fractional derivative Hadamard inequalities for m-convex and convex functions. Also, error...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/6642655 |
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| _version_ | 1832561305724125184 |
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| author | Xue Feng Baolin Feng Ghulam Farid Sidra Bibi Qi Xiaoyan Ze Wu |
| author_facet | Xue Feng Baolin Feng Ghulam Farid Sidra Bibi Qi Xiaoyan Ze Wu |
| author_sort | Xue Feng |
| collection | DOAJ |
| description | In this paper, two versions of the Hadamard inequality are obtained by using Caputo fractional derivatives and strongly m-convex functions. The established results will provide refinements of well-known Caputo fractional derivative Hadamard inequalities for m-convex and convex functions. Also, error estimations of Caputo fractional derivative Hadamard inequalities are proved and show that these are better than error estimations already existing in literature. |
| format | Article |
| id | doaj-art-9f96170895304967a34466ed0269f3d8 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-9f96170895304967a34466ed0269f3d82025-02-03T01:25:26ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/66426556642655Caputo Fractional Derivative Hadamard Inequalities for Strongly m-Convex FunctionsXue Feng0Baolin Feng1Ghulam Farid2Sidra Bibi3Qi Xiaoyan4Ze Wu5Aviation University of Air Force, Fundamental Departmental, Changchun, Jilin 130000, ChinaMudanjiang Normal University, School of Mathematical Sciences Mudanjiang, Heilongjiang 157011, ChinaDepartment of Mathematics, COMSATS University Islamabad, Attock Campus, PakistanGovt. Girls Primary School, Kamra Khurd, Attock 43570, PakistanAviation University of Air Force, Fundamental Departmental, Changchun, Jilin 130000, ChinaAviation University of Air Force, Fundamental Departmental, Changchun, Jilin 130000, ChinaIn this paper, two versions of the Hadamard inequality are obtained by using Caputo fractional derivatives and strongly m-convex functions. The established results will provide refinements of well-known Caputo fractional derivative Hadamard inequalities for m-convex and convex functions. Also, error estimations of Caputo fractional derivative Hadamard inequalities are proved and show that these are better than error estimations already existing in literature.http://dx.doi.org/10.1155/2021/6642655 |
| spellingShingle | Xue Feng Baolin Feng Ghulam Farid Sidra Bibi Qi Xiaoyan Ze Wu Caputo Fractional Derivative Hadamard Inequalities for Strongly m-Convex Functions Journal of Function Spaces |
| title | Caputo Fractional Derivative Hadamard Inequalities for Strongly m-Convex Functions |
| title_full | Caputo Fractional Derivative Hadamard Inequalities for Strongly m-Convex Functions |
| title_fullStr | Caputo Fractional Derivative Hadamard Inequalities for Strongly m-Convex Functions |
| title_full_unstemmed | Caputo Fractional Derivative Hadamard Inequalities for Strongly m-Convex Functions |
| title_short | Caputo Fractional Derivative Hadamard Inequalities for Strongly m-Convex Functions |
| title_sort | caputo fractional derivative hadamard inequalities for strongly m convex functions |
| url | http://dx.doi.org/10.1155/2021/6642655 |
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