A characterization of convex function

Xin Min Yang; Kok Lay Teo; Xiaoqi Yang

doi:10.1016/S0893-9659(99)00140-8

A characterization of convex function

Xin Min Yang, Kok Lay Teo, Xiaoqi Yang

Research output: Journal article publication › Journal article › Academic research › peer-review

13 Citations (Scopus)

Abstract

If C ⊆ ℛScript n sign be a nonempty convex set, then f : C → ℛ is convex function if and only if it is a quasiconvex function on C and there exists some α ∈ (0, 1) such that f(αx + (1 - α)y) ≤ αf(x) + (1 - α)f(y), ∀ x, y ∈ C.

Original language	English
Pages (from-to)	27-30
Number of pages	4
Journal	Applied Mathematics Letters
Volume	13
Issue number	1
DOIs	https://doi.org/10.1016/S0893-9659(99)00140-8
Publication status	Published - 11 Oct 1999

Keywords

Characterization
Convex function
Convex set
Intermediate-point convexity
Quasiconvex function

ASJC Scopus subject areas

Applied Mathematics

More information

10.1016/S0893-9659(99)00140-8

Cite this

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title = "A characterization of convex function",

abstract = "If C ⊆ ℛScript n sign be a nonempty convex set, then f : C → ℛ is convex function if and only if it is a quasiconvex function on C and there exists some α ∈ (0, 1) such that f(αx + (1 - α)y) ≤ αf(x) + (1 - α)f(y), ∀ x, y ∈ C.",

keywords = "Characterization, Convex function, Convex set, Intermediate-point convexity, Quasiconvex function",

author = "Yang, \{Xin Min\} and Teo, \{Kok Lay\} and Xiaoqi Yang",

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AU - Teo, Kok Lay

AU - Yang, Xiaoqi

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N2 - If C ⊆ ℛScript n sign be a nonempty convex set, then f : C → ℛ is convex function if and only if it is a quasiconvex function on C and there exists some α ∈ (0, 1) such that f(αx + (1 - α)y) ≤ αf(x) + (1 - α)f(y), ∀ x, y ∈ C.

AB - If C ⊆ ℛScript n sign be a nonempty convex set, then f : C → ℛ is convex function if and only if it is a quasiconvex function on C and there exists some α ∈ (0, 1) such that f(αx + (1 - α)y) ≤ αf(x) + (1 - α)f(y), ∀ x, y ∈ C.

KW - Characterization

KW - Convex function

KW - Convex set

KW - Intermediate-point convexity

KW - Quasiconvex function

UR - https://www.scopus.com/pages/publications/0041027494

U2 - 10.1016/S0893-9659(99)00140-8

DO - 10.1016/S0893-9659(99)00140-8

M3 - Journal article

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VL - 13

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EP - 30

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 1

ER -

A characterization of convex function

Abstract

Keywords

ASJC Scopus subject areas

More information

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