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On some generalizations of convex sets and convex functions

På svenska

Author

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.

Publishing year

1985

Language

English

Pages

1-6

Publication/Series

L'analyse numérique et la théorie de l'approximation

Volume

14

Issue

1

Document type

Journal article

Publisher

Cluj University Press

Topic

  • Mathematics

Status

Published

ISBN/ISSN/Other

  • ISSN: 1010-3376