On some generalizations of convex sets and convex functions

Summary, in 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.

• Författare: Alexandru Aleman
• Publiceringsår: 1985
• Språk: Engelska
• Sidor: 1-6
• Publikation/Tidskrift/Serie: L'analyse numérique et la théorie de l'approximation
• Volym: 14
• Issue: 1
• Dokumenttyp: Artikel i tidskrift
• Förlag: Cluj University Press
• Ämne: Mathematics
• Status: Published
• ISBN/ISSN/Övrigt: ISSN: 1010-3376