Some properties of set-valued sine families
Let \(\{F_t : t \geq 0\}\) be a family of continuous additive set-valued functions defined on a convex cone \(K\) in a normed linear space \(X\) with nonempty convex compact values in \(X\). It is shown that (under some assumptions) a regular sine family associated with \(\{F_t : t \geq 0\}\) is co...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2012-01-01
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| Series: | Opuscula Mathematica |
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| Online Access: | http://www.opuscula.agh.edu.pl/vol32/1/art/opuscula_math_3213.pdf |
| _version_ | 1819240264240201728 |
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| author | Ewelina Mainka-Niemczyk |
| author_facet | Ewelina Mainka-Niemczyk |
| author_sort | Ewelina Mainka-Niemczyk |
| collection | DOAJ |
| description | Let \(\{F_t : t \geq 0\}\) be a family of continuous additive set-valued functions defined on a convex cone \(K\) in a normed linear space \(X\) with nonempty convex compact values in \(X\). It is shown that (under some assumptions) a regular sine family associated with \(\{F_t : t \geq 0\}\) is continuous and \(\{F_t : t \geq 0\}\) is a continuous cosine family. |
| first_indexed | 2024-12-23T14:05:15Z |
| format | Article |
| id | doaj.art-f5df049578af4ad6bb451588fd268ff1 |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-12-23T14:05:15Z |
| publishDate | 2012-01-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-f5df049578af4ad6bb451588fd268ff12022-12-21T17:44:12ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742012-01-01321159170http://dx.doi.org/10.7494/OpMath.2012.32.1.1593213Some properties of set-valued sine familiesEwelina Mainka-Niemczyk0Silesian University of Technology, Institute of Mathematics, Kaszubska 23, 44-100 Gliwice, PolandLet \(\{F_t : t \geq 0\}\) be a family of continuous additive set-valued functions defined on a convex cone \(K\) in a normed linear space \(X\) with nonempty convex compact values in \(X\). It is shown that (under some assumptions) a regular sine family associated with \(\{F_t : t \geq 0\}\) is continuous and \(\{F_t : t \geq 0\}\) is a continuous cosine family.http://www.opuscula.agh.edu.pl/vol32/1/art/opuscula_math_3213.pdfset-valued sine and cosine familiescontinuity of sine familiesHukuhara differencesconcave set-valued functions |
| spellingShingle | Ewelina Mainka-Niemczyk Some properties of set-valued sine families Opuscula Mathematica set-valued sine and cosine families continuity of sine families Hukuhara differences concave set-valued functions |
| title | Some properties of set-valued sine families |
| title_full | Some properties of set-valued sine families |
| title_fullStr | Some properties of set-valued sine families |
| title_full_unstemmed | Some properties of set-valued sine families |
| title_short | Some properties of set-valued sine families |
| title_sort | some properties of set valued sine families |
| topic | set-valued sine and cosine families continuity of sine families Hukuhara differences concave set-valued functions |
| url | http://www.opuscula.agh.edu.pl/vol32/1/art/opuscula_math_3213.pdf |
| work_keys_str_mv | AT ewelinamainkaniemczyk somepropertiesofsetvaluedsinefamilies |