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, issue 1

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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https://doi.org/10.1155/2021/5529796

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2021:y:2021:i:1:n:5529796

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