An Extension of the Carathéodory Differentiability to Set-Valued Maps

Pedro Hurtado, Alexander Leones, M. Martelo and J. B. Moreno

Abstract and Applied Analysis, 2021, vol. 2021, 1-8

Abstract:

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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:5529796

DOI: 10.1155/2021/5529796

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