An Extension of the Carathéodory Differentiability to Set-Valued Maps | Zendy

Pedro Hurtado | Zendy; Alexander Leones | Zendy; Mitchael Martelo | Zendy; John Moreno | Zendy

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An Extension of the Carathéodory Differentiability to Set-Valued Maps

Author(s) -

Pedro Hurtado,

Alexander Leones,

Mitchael Martelo,

John Moreno

Publication year - 2021

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2021/5529796

Subject(s) - mathematics , differentiable function , generalization , extension (predicate logic) , pure mathematics , affine transformation , set (abstract data type) , mathematical analysis , computer science , programming language

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.

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