On a Separation Theorem for Delta-Convex Functions
In the present paper we establish necessary and sufficient conditions under which two functions can be separated by a delta-convex function. This separation will be understood as a separation with respect to the partial order generated by the Lorentz cone. An application to a stability problem for d...
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| Format: | Article |
| Language: | English |
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Sciendo
2020-07-01
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| Series: | Annales Mathematicae Silesianae |
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| Online Access: | http://www.degruyter.com/view/j/amsil.2020.34.issue-1/amsil-2020-0013/amsil-2020-0013.xml?format=INT |
| _version_ | 1819109994039083008 |
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| author | Olbryś Andrzej |
| author_facet | Olbryś Andrzej |
| author_sort | Olbryś Andrzej |
| collection | DOAJ |
| description | In the present paper we establish necessary and sufficient conditions under which two functions can be separated by a delta-convex function. This separation will be understood as a separation with respect to the partial order generated by the Lorentz cone. An application to a stability problem for delta-convexity is also given. |
| first_indexed | 2024-12-22T03:34:40Z |
| format | Article |
| id | doaj.art-d7ef73edb042443e8e47d8353b563476 |
| institution | Directory Open Access Journal |
| issn | 2391-4238 |
| language | English |
| last_indexed | 2024-12-22T03:34:40Z |
| publishDate | 2020-07-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Annales Mathematicae Silesianae |
| spelling | doaj.art-d7ef73edb042443e8e47d8353b5634762022-12-21T18:40:25ZengSciendoAnnales Mathematicae Silesianae2391-42382020-07-0134113314110.2478/amsil-2020-0013amsil-2020-0013On a Separation Theorem for Delta-Convex FunctionsOlbryś Andrzej0Institute of Mathematics, University of Silesia, Bankowa 14, 40-007Katowice, PolandIn the present paper we establish necessary and sufficient conditions under which two functions can be separated by a delta-convex function. This separation will be understood as a separation with respect to the partial order generated by the Lorentz cone. An application to a stability problem for delta-convexity is also given.http://www.degruyter.com/view/j/amsil.2020.34.issue-1/amsil-2020-0013/amsil-2020-0013.xml?format=INTconvex functinsdelta-convex functionlorentz cone26a5139b6226b2539b22 |
| spellingShingle | Olbryś Andrzej On a Separation Theorem for Delta-Convex Functions Annales Mathematicae Silesianae convex functins delta-convex function lorentz cone 26a51 39b62 26b25 39b22 |
| title | On a Separation Theorem for Delta-Convex Functions |
| title_full | On a Separation Theorem for Delta-Convex Functions |
| title_fullStr | On a Separation Theorem for Delta-Convex Functions |
| title_full_unstemmed | On a Separation Theorem for Delta-Convex Functions |
| title_short | On a Separation Theorem for Delta-Convex Functions |
| title_sort | on a separation theorem for delta convex functions |
| topic | convex functins delta-convex function lorentz cone 26a51 39b62 26b25 39b22 |
| url | http://www.degruyter.com/view/j/amsil.2020.34.issue-1/amsil-2020-0013/amsil-2020-0013.xml?format=INT |
| work_keys_str_mv | AT olbrysandrzej onaseparationtheoremfordeltaconvexfunctions |