An Extension of the Carathéodory Differentiability to Set-Valued Maps

This paper uses the generalization of the Hukuhara difference for compact convex set to extend the classical notions of Carathéodory differentiability to multifunctions (set-valued maps). Using the Hukuhara difference and affine multifunctions as a local approximation, we introduce the notion of CH-...

Full description

Saved in:
Bibliographic Details
Published in:Abstract and applied analysis 2021, Vol.2021, p.1-8
Main Authors: Hurtado, Pedro, Leones, Alexander, Martelo, M., Moreno, J. B.
Format: Article
Language:English
Subjects:
Control theory
Convex sets
Euclidean space
Functional equations
Functions
Mappings (Mathematics)
Mathematical research
Ordinary differential equations
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper uses the generalization of the Hukuhara difference for compact convex set to extend the classical notions of Carathéodory differentiability to multifunctions (set-valued maps). Using the Hukuhara difference and affine multifunctions as a local approximation, we introduce the notion of CH-differentiability for multifunctions. Finally, we tackle the study of the relation among the Fréchet differentiability, Hukuhara differentiability, and CH-differentiability.
ISSN:1085-3375
1687-0409
DOI:10.1155/2021/5529796