A characterization of C1,1 functions via lower directional derivatives

Title:

A characterization of C1,1 functions via lower directional derivatives

Creator:

Bednařík, Dušan and Pastor, Karel

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:01fde510-adb5-4bda-b102-2c7db2f1e4ae
uuid:01fde510-adb5-4bda-b102-2c7db2f1e4ae
doi:10.21136/MB.2009.140656

Subject:

second-order derivative, C 1,1 function, ℓ-stable function, and ˜ℓ-stability

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

The notion of ˜ℓ-stability is defined using the lower Dini directional derivatives and was introduced by the authors in their previous papers. In this paper we prove that the class of ˜ℓ-stable functions coincides with the class of C1,1 functions. This also solves the question posed by the authors in SIAM J. Control Optim. 45 (1) (2006), pp. 383–387.

Language:

English

Rights:

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

Coverage:

217-221

Source:

Mathematica bohemica | 2009 Volume:134 | Number:2

Harvested from:

CDK

Metadata only:

false