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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.00293 |
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| _version_ | 1866914625936687104 |
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| author | Tran, Nguyen B. Nguyen, Tran N. Hien, Huynh M. |
| author_facet | Tran, Nguyen B. Nguyen, Tran N. Hien, Huynh M. |
| contents | This work deals with a maximal monotone operator $A$ of type (D) in a Banach space whose dual space is strictly convex. We establish some representations for the value $Ax$ at a given point $x$ via its values at nearby points of $x$. We show that the faces of $Ax$ are contained in the set of all weak$^*$ convergent limits of bounded nets of the operator at nearby points of $x$, then we obtain a representation for $Ax$ by use of this set. In addition, representations for the support function of $Ax$ based on the minimal-norm selection of the operator in certain Banach spaces are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00293 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Representation formulas for maximal monotone operators of type (D) in Banach spaces whose dual spaces are strictly convex Tran, Nguyen B. Nguyen, Tran N. Hien, Huynh M. Functional Analysis Optimization and Control 47H05, 47H04, 47N10 This work deals with a maximal monotone operator $A$ of type (D) in a Banach space whose dual space is strictly convex. We establish some representations for the value $Ax$ at a given point $x$ via its values at nearby points of $x$. We show that the faces of $Ax$ are contained in the set of all weak$^*$ convergent limits of bounded nets of the operator at nearby points of $x$, then we obtain a representation for $Ax$ by use of this set. In addition, representations for the support function of $Ax$ based on the minimal-norm selection of the operator in certain Banach spaces are given. |
| title | Representation formulas for maximal monotone operators of type (D) in Banach spaces whose dual spaces are strictly convex |
| topic | Functional Analysis Optimization and Control 47H05, 47H04, 47N10 |
| url | https://arxiv.org/abs/2401.00293 |