Higher order strongly general convex functions and variational inequalities
In this paper, we define and consider some new concepts of the higher order strongly general convex functions with respect to an arbitrary function. Some properties of the higher order strongly general convex functions are investigated under suitable conditions. It is shown that the optimality condi...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-05-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/10.3934/math.2020236/fulltext.html |
| _version_ | 1819225886785798144 |
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| author | Muhammad Aslam Noor Khalida Inayat Noor |
| author_facet | Muhammad Aslam Noor Khalida Inayat Noor |
| author_sort | Muhammad Aslam Noor |
| collection | DOAJ |
| description | In this paper, we define and consider some new concepts of the higher order strongly general convex functions with respect to an arbitrary function. Some properties of the higher order strongly general convex functions are investigated under suitable conditions. It is shown that the optimality conditions of the higher order strongly general convex functions are characterized by a class of variational inequalities, which is called the higher order strongly variational inequality. Auxiliary principle technique is used to suggest an implicit method for solving strongly general variational inequalities. Convergence analysis of the proposed method is investigated using the pseudo-monotonicity of the operator. It is shown that the parallelogram laws for Banach spaces can be obtained as applications of higher order strongly affine convex functions. Some special cases also discussed. Results obtained in this paper can be viewed as refinement and improvement of previously known results. |
| first_indexed | 2024-12-23T10:16:43Z |
| format | Article |
| id | doaj.art-a4549ec569304cc99b8baa374b793127 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-23T10:16:43Z |
| publishDate | 2020-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-a4549ec569304cc99b8baa374b7931272022-12-21T17:50:47ZengAIMS PressAIMS Mathematics2473-69882020-05-01543646366310.3934/math.2020236Higher order strongly general convex functions and variational inequalitiesMuhammad Aslam Noor0Khalida Inayat Noor1Department of Mathematics, COMSATS University Islamabad, Islamabad, PakistanDepartment of Mathematics, COMSATS University Islamabad, Islamabad, PakistanIn this paper, we define and consider some new concepts of the higher order strongly general convex functions with respect to an arbitrary function. Some properties of the higher order strongly general convex functions are investigated under suitable conditions. It is shown that the optimality conditions of the higher order strongly general convex functions are characterized by a class of variational inequalities, which is called the higher order strongly variational inequality. Auxiliary principle technique is used to suggest an implicit method for solving strongly general variational inequalities. Convergence analysis of the proposed method is investigated using the pseudo-monotonicity of the operator. It is shown that the parallelogram laws for Banach spaces can be obtained as applications of higher order strongly affine convex functions. Some special cases also discussed. Results obtained in this paper can be viewed as refinement and improvement of previously known results.https://www.aimspress.com/article/10.3934/math.2020236/fulltext.htmlhigher order convex functionsvariational inequalitiesparallelogram laws |
| spellingShingle | Muhammad Aslam Noor Khalida Inayat Noor Higher order strongly general convex functions and variational inequalities AIMS Mathematics higher order convex functions variational inequalities parallelogram laws |
| title | Higher order strongly general convex functions and variational inequalities |
| title_full | Higher order strongly general convex functions and variational inequalities |
| title_fullStr | Higher order strongly general convex functions and variational inequalities |
| title_full_unstemmed | Higher order strongly general convex functions and variational inequalities |
| title_short | Higher order strongly general convex functions and variational inequalities |
| title_sort | higher order strongly general convex functions and variational inequalities |
| topic | higher order convex functions variational inequalities parallelogram laws |
| url | https://www.aimspress.com/article/10.3934/math.2020236/fulltext.html |
| work_keys_str_mv | AT muhammadaslamnoor higherorderstronglygeneralconvexfunctionsandvariationalinequalities AT khalidainayatnoor higherorderstronglygeneralconvexfunctionsandvariationalinequalities |