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.
| Original language | English |
|---|---|
| Pages (from-to) | 1-6 |
| Journal | L'analyse numérique et la théorie de l'approximation |
| Volume | 14 |
| Issue number | 1 |
| Publication status | Published - 1985 |
| Externally published | Yes |
Bibliographical note
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.
Subject classification (UKÄ)
- Mathematics