Advanced

On some generalizations of convex sets and convex functions

Aleman, Alexandru LU (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:
author
publishing date
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},
}