On a theorem about Mosco convergence in Hadamard spaces
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866909531949236224 |
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| author | Berdellima, Arian |
| author_facet | Berdellima, Arian |
| contents | Let $(f^n),f$ be a sequence of proper closed convex functions defined on a Hadamard space. We show that the convergence of proximal mappings $J^n_λx$ to $J_λx$, under certain additional conditions, imply Mosco convergence of $f^n$ to $f$. This result is a converse to a theorem of Bacak about Mosco convergence in Hadamard spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_05554 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On a theorem about Mosco convergence in Hadamard spaces Berdellima, Arian Functional Analysis Metric Geometry 47H09, 46N10, 30L05 Let $(f^n),f$ be a sequence of proper closed convex functions defined on a Hadamard space. We show that the convergence of proximal mappings $J^n_λx$ to $J_λx$, under certain additional conditions, imply Mosco convergence of $f^n$ to $f$. This result is a converse to a theorem of Bacak about Mosco convergence in Hadamard spaces. |
| title | On a theorem about Mosco convergence in Hadamard spaces |
| topic | Functional Analysis Metric Geometry 47H09, 46N10, 30L05 |
| url | https://arxiv.org/abs/2010.05554 |