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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2405.13510 |
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| _version_ | 1866909209007751168 |
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| author | Alwadani, Salihah Thabet |
| author_facet | Alwadani, Salihah Thabet |
| contents | The theory of monotone operators plays a major role in modern optimization and many areas of nonlinera analysis. The central classes of monotone operators are matrices with a positive semidefinite symmetric part and subsifferential operators. In this paper, we complete our study to the displacement mappings. We derive formulas for set-valued and Moore-Penrose inverses. We also give a comprehensive study of the the operators ($(1/2) {\rm Id} + T$ and its inverse) and provide a formula for $((1/2) {\rm Id} + T)^{-1}$. We illustrate our results by considering the reflected and the projection operators to closed linear subspaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_13510 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Additional Studies on Displacement Mapping with Restrictions Alwadani, Salihah Thabet Functional Analysis The theory of monotone operators plays a major role in modern optimization and many areas of nonlinera analysis. The central classes of monotone operators are matrices with a positive semidefinite symmetric part and subsifferential operators. In this paper, we complete our study to the displacement mappings. We derive formulas for set-valued and Moore-Penrose inverses. We also give a comprehensive study of the the operators ($(1/2) {\rm Id} + T$ and its inverse) and provide a formula for $((1/2) {\rm Id} + T)^{-1}$. We illustrate our results by considering the reflected and the projection operators to closed linear subspaces. |
| title | Additional Studies on Displacement Mapping with Restrictions |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2405.13510 |