On some generalizations of convex sets and convex functions

Alexandru Aleman

On some generalizations of convex sets and convex functions

External Organization - Unknown

Research output: Contribution to journal › Article › peer-review

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)

Mathematical Sciences

Cite this

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title = "On some generalizations of convex sets and convex functions",

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\textbackslash{}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 = "Alexandru Aleman",

note = "Continues Revue d'analyse num{\'e}rique et de th{\'e}orie de l'approximation (1972) [ISSN 0301-9241] Continued by Revue d'analyse num{\'e}rique et de th{\'e}orie de l'approximation (1992) [ISSN 1222-9024] Varianttitlar * Mathematica - Revue d'analyse num{\'e}rique et de th{\'e}orie de l'approximation / Acad{\'e}mie de la R{\'e}publique Socialiste de Roumanie, Filiale de Cluj-Napoca. L'analyse num{\'e}rique et la th{\'e}orie de l'approximation.",

year = "1985",

language = "English",

volume = "14",

pages = "1--6",

journal = "L'analyse num{\'e}rique et la th{\'e}orie de l'approximation",

issn = "1010-3376",

publisher = "Cluj University Press",

number = "1",

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AU - Aleman, Alexandru

N1 - 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.

PY - 1985

Y1 - 1985

N2 - 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.

AB - 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.

M3 - Article

SN - 1010-3376

VL - 14

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EP - 6

JO - L'analyse numérique et la théorie de l'approximation

JF - L'analyse numérique et la théorie de l'approximation

IS - 1

ER -

On some generalizations of convex sets and convex functions

Abstract

Bibliographical note

Subject classification (UKÄ)

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