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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.
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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
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}},
}