| Title | On some generalizations of convex sets and convex functions |
| Authors | Alexandru Aleman |
| Publication | L'analyse numérique et la théorie de l'approximation |
| Year | 1985 |
| Volume | 14 |
| Issue | 1 |
| Pages | 1 - 6 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Cluj-Napoca :Éd. de l'Académie de la République Socialiste de Roumanie,1975-1991 |
| Abstract English | 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. |
| ISBN/ISSN/Other | ISSN: 1010-3376 |
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