On Long Orbit Empty Value (LOEV) principle
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916813992886272 |
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| author | Ivanov, M. Kamburova, D. Zlateva, N. |
| author_facet | Ivanov, M. Kamburova, D. Zlateva, N. |
| contents | We consider an useful in Variational Analysis tool -- Long Orbit or Empty Value (LOEV) principle -- in different settings, starting from more abstract to more defined.
We prove, using LOEV principle, a number of basic results in Variational Analysis, including some novel. We characterize $Σ_g$-semicompleteness for a generalized metric function $g$ which is neither symmetric nor satisfies the triangle inequality, in terms of validity of Ekeland Theorem for this $g$. We present an interesting application to perturbability to minimum in a $G_δ$ subset of a complete metric space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07189 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Long Orbit Empty Value (LOEV) principle Ivanov, M. Kamburova, D. Zlateva, N. Functional Analysis 49J53, 54E25, 47H10, 58E30 We consider an useful in Variational Analysis tool -- Long Orbit or Empty Value (LOEV) principle -- in different settings, starting from more abstract to more defined. We prove, using LOEV principle, a number of basic results in Variational Analysis, including some novel. We characterize $Σ_g$-semicompleteness for a generalized metric function $g$ which is neither symmetric nor satisfies the triangle inequality, in terms of validity of Ekeland Theorem for this $g$. We present an interesting application to perturbability to minimum in a $G_δ$ subset of a complete metric space. |
| title | On Long Orbit Empty Value (LOEV) principle |
| topic | Functional Analysis 49J53, 54E25, 47H10, 58E30 |
| url | https://arxiv.org/abs/2407.07189 |