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:
http://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
- id
- 79eda3c8-d675-4a6c-9832-f256ae522361 (old id 1467387)
- date added to LUP
- 2009-09-16 14:36:52
- date last changed
- 2016-06-29 08:57:33
@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}, }