ABSOLUTE DERIVATIVE OF SET-VALUED MAPS

Mohamad Muslikh; Adem Kilicman

doi:10.54671/BMAA-2022-3-2

ABSOLUTE DERIVATIVE OF SET-VALUED MAPS

Mohamad Muslikh
, Adem Kilicman

Faculty of Mathematics and Natural Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

The aim of this article is to develop a differential calculus for setvalued functions with values in metric spaces of the family of all compact and convex subsets. Using only the metric Hausdorff on metric spaces and without using the Hukuhara difference, a concept of the derivative is introduced for set-valued functions in such metric spaces. The comparison with the other derivative definitions of the set-valued functions and the relation to the Lipschitz conditions was also investigated in this paper.

Original language	English
Pages (from-to)	20-35
Number of pages	16
Journal	Bulletin of Mathematical Analysis and Applications
Volume	14
Issue number	3
DOIs	https://doi.org/10.54671/BMAA-2022-3-2
Publication status	Published - 2022

Keywords

Defferentiation
Set-valued

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10.54671/BMAA-2022-3-2

Cite this

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abstract = "The aim of this article is to develop a differential calculus for setvalued functions with values in metric spaces of the family of all compact and convex subsets. Using only the metric Hausdorff on metric spaces and without using the Hukuhara difference, a concept of the derivative is introduced for set-valued functions in such metric spaces. The comparison with the other derivative definitions of the set-valued functions and the relation to the Lipschitz conditions was also investigated in this paper.",

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AU - Muslikh, Mohamad

AU - Kilicman, Adem

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N2 - The aim of this article is to develop a differential calculus for setvalued functions with values in metric spaces of the family of all compact and convex subsets. Using only the metric Hausdorff on metric spaces and without using the Hukuhara difference, a concept of the derivative is introduced for set-valued functions in such metric spaces. The comparison with the other derivative definitions of the set-valued functions and the relation to the Lipschitz conditions was also investigated in this paper.

AB - The aim of this article is to develop a differential calculus for setvalued functions with values in metric spaces of the family of all compact and convex subsets. Using only the metric Hausdorff on metric spaces and without using the Hukuhara difference, a concept of the derivative is introduced for set-valued functions in such metric spaces. The comparison with the other derivative definitions of the set-valued functions and the relation to the Lipschitz conditions was also investigated in this paper.

KW - Defferentiation

KW - Set-valued

UR - https://www.scopus.com/pages/publications/85161293713

U2 - 10.54671/BMAA-2022-3-2

DO - 10.54671/BMAA-2022-3-2

M3 - Article

AN - SCOPUS:85161293713

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EP - 35

JO - Bulletin of Mathematical Analysis and Applications

JF - Bulletin of Mathematical Analysis and Applications

IS - 3

ER -

ABSOLUTE DERIVATIVE OF SET-VALUED MAPS

Abstract

Keywords

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