On some generalizations of convex sets and convex functions
(1985) In L'analyse numérique et la théorie de l'approximation 14(1). p.1-6- Abstract
- A set $C$ in a topological vector space is said to be weakly convex if for any $x,y$ in $C$ there exists $p$ in $(0,1)$ such that $(1-p)x+py\in C$. If the same holds with $p$ independent of $x,y$, then $C$ is said to be $p$-convex. Some basic results are established for such sets, for instance: any weakly convex closed set is convex.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1467387
- author
- Aleman, Alexandru LU
- publishing date
- 1985
- type
- Contribution to journal
- publication status
- published
- subject
- in
- L'analyse numérique et la théorie de l'approximation
- volume
- 14
- issue
- 1
- pages
- 1 - 6
- publisher
- Cluj University Press
- ISSN
- 1010-3376
- language
- English
- LU publication?
- no
- additional info
- Continues Revue d'analyse numérique et de théorie de l'approximation (1972) [ISSN 0301-9241] Continued by Revue d'analyse numérique et de théorie de l'approximation (1992) [ISSN 1222-9024] Varianttitlar * Mathematica - Revue d'analyse numérique et de théorie de l'approximation / Académie de la République Socialiste de Roumanie, Filiale de Cluj-Napoca. L'analyse numérique et la théorie de l'approximation.
- id
- 79eda3c8-d675-4a6c-9832-f256ae522361 (old id 1467387)
- date added to LUP
- 2016-04-01 15:30:39
- date last changed
- 2018-11-21 20:34:49
@article{79eda3c8-d675-4a6c-9832-f256ae522361, abstract = {{A set $C$ in a topological vector space is said to be weakly convex if for any $x,y$ in $C$ there exists $p$ in $(0,1)$ such that $(1-p)x+py\in C$. If the same holds with $p$ independent of $x,y$, then $C$ is said to be $p$-convex. Some basic results are established for such sets, for instance: any weakly convex closed set is convex.}}, author = {{Aleman, Alexandru}}, issn = {{1010-3376}}, language = {{eng}}, number = {{1}}, pages = {{1--6}}, publisher = {{Cluj University Press}}, series = {{L'analyse numérique et la théorie de l'approximation}}, title = {{On some generalizations of convex sets and convex functions}}, volume = {{14}}, year = {{1985}}, }