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http://hdl.handle.net/11320/21472Pełny rekord metadanych
| Pole DC | Wartość | Język |
|---|---|---|
| dc.contributor.author | Endou, Noboru | - |
| dc.contributor.author | Mitsuishi, Takashi | - |
| dc.contributor.author | Shidama, Yasunari | - |
| dc.date.accessioned | 2026-11-09T10:08:36Z | - |
| dc.date.available | 2026-11-09T10:08:36Z | - |
| dc.date.issued | 2003 | - |
| dc.identifier.citation | Formalized Mathematics, Volume 11, Issue 1, Pages 53-58 | pl |
| dc.identifier.issn | 1426-2630 | - |
| dc.identifier.uri | http://hdl.handle.net/11320/21472 | - |
| dc.description.abstract | Convexity is one of the most important concepts in a study of analysis. Especially, it has been applied around the optimization problem widely. Our purpose is to define the concept of convexity of a set on Mizar, and to develop the generalities of convex analysis. The construction of this article is as follows: Convexity of the set is defined in the section 1. The section 2 gives the definition of convex combination which is a kind of the linear combination and related theorems are proved there. In section 3, we define the convex hull which is an intersection of all convex sets including a given set. The last section is some theorems which are necessary to compose this article. | pl |
| dc.language.iso | en | pl |
| dc.publisher | University of Białystok | pl |
| dc.rights | CC BY-SA 4.0 | - |
| dc.rights.uri | https://creativecommons.org/licenses/by-sa/4.0/ | - |
| dc.title | Convex Sets and Convex Combinations | pl |
| dc.type | Article | pl |
| dc.rights.holder | © 2003 University of Białystok | pl |
| dc.rights.holder | This work is licensed under the Creative Commons License. | pl |
| dc.description.Affiliation | Noboru Endou - Gifu National College of Technology | pl |
| dc.description.Affiliation | Takashi Mitsuishi - Miyagi University | pl |
| dc.description.Affiliation | Yasunari Shidama - Shinshu University Nagano | pl |
| dc.description.references | Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377–382, 1990. | pl |
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| dc.description.references | Noboru Endou, Takashi Mitsuishi, and Yasunari Shidama. Dimension of real unitary space. Formalized Mathematics, 11(1):23–28, 2003. | pl |
| dc.description.references | Noboru Endou, Takashi Mitsuishi, and Yasunari Shidama. Topology of real unitary space. Formalized Mathematics, 11(1):33–38, 2003. | pl |
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| dc.description.references | Andrzej Trybulec. Enumerated sets. Formalized Mathematics, 1(1):25–34, 1990. | pl |
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| dc.description.references | Wojciech A. Trybulec. Linear combinations in real linear space. Formalized Mathematics, 1(3):581–588, 1990. | pl |
| dc.description.references | Wojciech A. Trybulec. Subspaces and cosets of subspaces in real linear space. Formalized Mathematics, 1(2):297–301, 1990. | pl |
| dc.description.references | Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291–296, 1990. | pl |
| dc.description.references | Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67–71, 1990. | pl |
| dc.identifier.eissn | 1898-9934 | - |
| dc.description.volume | 11 | pl |
| dc.description.issue | 1 | pl |
| dc.description.firstpage | 53 | pl |
| dc.description.lastpage | 58 | pl |
| dc.identifier.citation2 | Formalized Mathematics | pl |
| Występuje w kolekcji(ach): | Formalized Mathematics, 2003, Volume 11, Issue 1 | |
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|---|---|---|---|---|
| Convex_Sets_and_Convex_Combinations.pdf | 69,7 kB | Adobe PDF | Otwórz |
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