Generalization of Some Inequalities for Differentiable Co-ordinated Convex Functions With Applications
In this paper, a new weighted identity for functions defined on a rectangle from the plane is established. By using the obtained identity and analysis, some new weighted integral inequalities for the classes of co-ordinated convex, co-ordinated wright-convex and co-ordinated quasi-convex functions o...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Sciendo
2016-06-01
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| Series: | Moroccan Journal of Pure and Applied Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.7603/s40956-016-0002-4 |
| _version_ | 1811328264347582464 |
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| author | Latif M. A. Dragomir S. S. Momoniat E. |
| author_facet | Latif M. A. Dragomir S. S. Momoniat E. |
| author_sort | Latif M. A. |
| collection | DOAJ |
| description | In this paper, a new weighted identity for functions defined on a rectangle from the plane is established. By using the obtained identity and analysis, some new weighted integral inequalities for the classes of co-ordinated convex, co-ordinated wright-convex and co-ordinated quasi-convex functions on the rectangle from the plane are established which provide weighted generalization of some recent results proved for co-ordinated convex functions. Some applications of our results to random variables and 2D weighted quadrature formula are given as well. |
| first_indexed | 2024-04-13T15:22:12Z |
| format | Article |
| id | doaj.art-589b501cd27d46499e5360b1e99a96c6 |
| institution | Directory Open Access Journal |
| issn | 2351-8227 |
| language | English |
| last_indexed | 2024-04-13T15:22:12Z |
| publishDate | 2016-06-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Moroccan Journal of Pure and Applied Analysis |
| spelling | doaj.art-589b501cd27d46499e5360b1e99a96c62022-12-22T02:41:37ZengSciendoMoroccan Journal of Pure and Applied Analysis2351-82272016-06-0121123210.7603/s40956-016-0002-4Generalization of Some Inequalities for Differentiable Co-ordinated Convex Functions With ApplicationsLatif M. A.0Dragomir S. S.1Momoniat E.2School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South AfricaSchool of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa AustraliaSchool of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South AfricaIn this paper, a new weighted identity for functions defined on a rectangle from the plane is established. By using the obtained identity and analysis, some new weighted integral inequalities for the classes of co-ordinated convex, co-ordinated wright-convex and co-ordinated quasi-convex functions on the rectangle from the plane are established which provide weighted generalization of some recent results proved for co-ordinated convex functions. Some applications of our results to random variables and 2D weighted quadrature formula are given as well.https://doi.org/10.7603/s40956-016-0002-4hermite-hadamard’s inequalityco-ordinated convex functioncoordinated wright-convex functionco-ordinated quasi-convex functionhölder’s integral inequalityquadrature formula |
| spellingShingle | Latif M. A. Dragomir S. S. Momoniat E. Generalization of Some Inequalities for Differentiable Co-ordinated Convex Functions With Applications Moroccan Journal of Pure and Applied Analysis hermite-hadamard’s inequality co-ordinated convex function coordinated wright-convex function co-ordinated quasi-convex function hölder’s integral inequality quadrature formula |
| title | Generalization of Some Inequalities for Differentiable Co-ordinated Convex Functions With Applications |
| title_full | Generalization of Some Inequalities for Differentiable Co-ordinated Convex Functions With Applications |
| title_fullStr | Generalization of Some Inequalities for Differentiable Co-ordinated Convex Functions With Applications |
| title_full_unstemmed | Generalization of Some Inequalities for Differentiable Co-ordinated Convex Functions With Applications |
| title_short | Generalization of Some Inequalities for Differentiable Co-ordinated Convex Functions With Applications |
| title_sort | generalization of some inequalities for differentiable co ordinated convex functions with applications |
| topic | hermite-hadamard’s inequality co-ordinated convex function coordinated wright-convex function co-ordinated quasi-convex function hölder’s integral inequality quadrature formula |
| url | https://doi.org/10.7603/s40956-016-0002-4 |
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