Some Remarks on Results Related to ∇-Convex Function
In the present article, we give new techniques for proving general identities of the Popoviciu type for discrete cases of sums for two dimensions using higher-order ∇-divided difference. Also, integral cases are deduced by different methods for differentiable functions of higher-order for two variab...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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ITB Journal Publisher
2021-05-01
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| Series: | Journal of Mathematical and Fundamental Sciences |
| Subjects: | |
| Online Access: | https://journals.itb.ac.id/index.php/jmfs/article/view/9061 |
| _version_ | 1818330098828312576 |
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| author | Asif Raza Khan Faraz Mehmood Faisal Nawaz Aamna Nazir |
| author_facet | Asif Raza Khan Faraz Mehmood Faisal Nawaz Aamna Nazir |
| author_sort | Asif Raza Khan |
| collection | DOAJ |
| description | In the present article, we give new techniques for proving general identities of the Popoviciu type for discrete cases of sums for two dimensions using higher-order ∇-divided difference. Also, integral cases are deduced by different methods for differentiable functions of higher-order for two variables. These identities are a generalization of various previously established results. An application for the mean value theorem is also presented. |
| first_indexed | 2024-12-13T12:58:33Z |
| format | Article |
| id | doaj.art-c92c767d9332488a8ab23500ca8bebeb |
| institution | Directory Open Access Journal |
| issn | 2337-5760 2338-5510 |
| language | English |
| last_indexed | 2024-12-13T12:58:33Z |
| publishDate | 2021-05-01 |
| publisher | ITB Journal Publisher |
| record_format | Article |
| series | Journal of Mathematical and Fundamental Sciences |
| spelling | doaj.art-c92c767d9332488a8ab23500ca8bebeb2022-12-21T23:45:06ZengITB Journal PublisherJournal of Mathematical and Fundamental Sciences2337-57602338-55102021-05-0153110.5614/j.fund.math.sci.2021.53.1.5Some Remarks on Results Related to ∇-Convex FunctionAsif Raza Khan0Faraz Mehmood1Faisal Nawaz2Aamna Nazir3Department of Mathematics, University of Karachi, University Road, Karachi 75270, Pakistan Department of Mathematics, Dawood University of Engineering and Technology, New M.A. Jinnah Road, Karachi 74800, PakistanDepartment of Mathematics, Dawood University of Engineering and Technology, New M.A. Jinnah Road, Karachi 74800, PakistanDepartment of Mathematics, University of Karachi, University Road, Karachi 75270, Pakistan In the present article, we give new techniques for proving general identities of the Popoviciu type for discrete cases of sums for two dimensions using higher-order ∇-divided difference. Also, integral cases are deduced by different methods for differentiable functions of higher-order for two variables. These identities are a generalization of various previously established results. An application for the mean value theorem is also presented.https://journals.itb.ac.id/index.php/jmfs/article/view/9061convex function∇-convex function∇-operatordivided difference of a functionfinite difference of a function |
| spellingShingle | Asif Raza Khan Faraz Mehmood Faisal Nawaz Aamna Nazir Some Remarks on Results Related to ∇-Convex Function Journal of Mathematical and Fundamental Sciences convex function ∇-convex function ∇-operator divided difference of a function finite difference of a function |
| title | Some Remarks on Results Related to ∇-Convex Function |
| title_full | Some Remarks on Results Related to ∇-Convex Function |
| title_fullStr | Some Remarks on Results Related to ∇-Convex Function |
| title_full_unstemmed | Some Remarks on Results Related to ∇-Convex Function |
| title_short | Some Remarks on Results Related to ∇-Convex Function |
| title_sort | some remarks on results related to ∇ convex function |
| topic | convex function ∇-convex function ∇-operator divided difference of a function finite difference of a function |
| url | https://journals.itb.ac.id/index.php/jmfs/article/view/9061 |
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