Chain rule for conic derivatives

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F13%3A%230000398" target="_blank" >RIV/47813059:19610/13:#0000398 - isvavai.cz</a>

Result on the web

<a href="http://link.springer.com/article/10.1134%2FS0001434613030206" target="_blank" >http://link.springer.com/article/10.1134%2FS0001434613030206</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1134/S0001434613030206" target="_blank" >10.1134/S0001434613030206</a>

Result language

angličtina

Original language name

Chain rule for conic derivatives

Original language description

For all "nice" definitions of differentiability, the Chain Rule should be valid. We show that the Chain Rule remains true for some wide class of definitions of differentiability if one considers as approximative mappings (derivatives) not just continuouslinear, but positively homogeneous mappings satisfying certain topological conditions (which are fulfilled for continuous linear mappings). For brevity, we call such derivatives conic. We will give corollaries for the case of conic differentiation of mappings between normed spaces, especially for the case of Fr,chet conic differentiation and compact conic differentiation.

Czech name

—

Czech description

—

Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

—

Project

—

Continuities

S - Specificky vyzkum na vysokych skolach

Publication year

2013

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Mathematical Notes

ISSN

0001-4346

e-ISSN

—

Volume of the periodical

93

Issue of the periodical within the volume

3-4

Country of publishing house

US - UNITED STATES

Number of pages

16

Pages from-to

523-538

UT code for WoS article

000317986600020

EID of the result in the Scopus database

—