On vector functions of bounded convexity

Title:

On vector functions of bounded convexity

Creator:

Veselý, Libor and Zajíček, Luděk

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:42d1b9ba-f23d-41c0-ab96-0da3a742651e
uuid:42d1b9ba-f23d-41c0-ab96-0da3a742651e
doi:10.21136/MB.2008.140621

Subject:

bounded convexity, delta-convex mapping, bounded variation, and Banach space

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Let X be a normed linear space. We investigate properties of vector functions F : [a, b] → X of bounded convexity. In particular, we prove that such functions coincide with the delta-convex mappings admitting a Lipschitz control function, and that convexity Kb a F is equal to the variation of F ′ + on [a, b). As an application, we give a simple alternative proof of an unpublished result of the first author, containing an estimate of convexity of a composed mapping.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

321-335

Source:

Mathematica bohemica | 2008 Volume:133 | Number:3

Harvested from:

CDK

Metadata only:

false