Epi-lower semicontinuous mappings and their properties (in Ukrainian)
We present a new concept of lower semicontinuity for vector-valued mappings, so-called lower epi-semicontinuity, which is closely related with the sequential closedness of epigraphs of these mappings. We consider the case when the mappings take values in a real Banach space Y partially ordered by a...
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| Format: | Article |
| Language: | deu |
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Ivan Franko National University of Lviv
2011-07-01
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| Series: | Математичні Студії |
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| Online Access: | http://matstud.org.ua/texts/2011/36_1/86-96.pdf |
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| author | A. V. Dovzhenko P. I. Kogut |
| author_facet | A. V. Dovzhenko P. I. Kogut |
| author_sort | A. V. Dovzhenko |
| collection | DOAJ |
| description | We present a new concept of lower semicontinuity for vector-valued mappings, so-called lower epi-semicontinuity, which is closely related with the sequential closedness of epigraphs of these mappings. We consider the case when the mappings take values in a real Banach space Y partially ordered by a closed convex pointed cone L, and we make no additional assumptions on topological interior of the ordering cone. We also study the comparison of the lower epi-semicontinuity with the classical notion of lower semicontinuity and its generalizations. |
| format | Article |
| id | doaj-art-7a7fea45e1ed41acb20e07a8c88d06ca |
| institution | Kabale University |
| issn | 1027-4634 |
| language | deu |
| publishDate | 2011-07-01 |
| publisher | Ivan Franko National University of Lviv |
| record_format | Article |
| series | Математичні Студії |
| spelling | doaj-art-7a7fea45e1ed41acb20e07a8c88d06ca2025-08-20T03:57:03ZdeuIvan Franko National University of LvivМатематичні Студії1027-46342011-07-013618696Epi-lower semicontinuous mappings and their properties (in Ukrainian)A. V. DovzhenkoP. I. KogutWe present a new concept of lower semicontinuity for vector-valued mappings, so-called lower epi-semicontinuity, which is closely related with the sequential closedness of epigraphs of these mappings. We consider the case when the mappings take values in a real Banach space Y partially ordered by a closed convex pointed cone L, and we make no additional assumptions on topological interior of the ordering cone. We also study the comparison of the lower epi-semicontinuity with the classical notion of lower semicontinuity and its generalizations.http://matstud.org.ua/texts/2011/36_1/86-96.pdfepi-semicontinuityvector-valued mappings |
| spellingShingle | A. V. Dovzhenko P. I. Kogut Epi-lower semicontinuous mappings and their properties (in Ukrainian) Математичні Студії epi-semicontinuity vector-valued mappings |
| title | Epi-lower semicontinuous mappings and their properties (in Ukrainian) |
| title_full | Epi-lower semicontinuous mappings and their properties (in Ukrainian) |
| title_fullStr | Epi-lower semicontinuous mappings and their properties (in Ukrainian) |
| title_full_unstemmed | Epi-lower semicontinuous mappings and their properties (in Ukrainian) |
| title_short | Epi-lower semicontinuous mappings and their properties (in Ukrainian) |
| title_sort | epi lower semicontinuous mappings and their properties in ukrainian |
| topic | epi-semicontinuity vector-valued mappings |
| url | http://matstud.org.ua/texts/2011/36_1/86-96.pdf |
| work_keys_str_mv | AT avdovzhenko epilowersemicontinuousmappingsandtheirpropertiesinukrainian AT pikogut epilowersemicontinuousmappingsandtheirpropertiesinukrainian |