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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi
Mohamad Muslikh
Department of Mathematics, Faculty of Mathematics and Sciences, Universitas Brawijaya, Malang
Mathematics

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Compare Bede-Gal Between dH Differentiability of Set Valued Functions Wildan Bagus Wicaksono; Mohamad Muslikh
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.38181

Abstract

This paper presents a comparative study between the Bede--Gal differentiability and the dH-differentiability for set-valued functions whose values belong to the family of nonempty compact convex subsets of $\mathbb{R}^n$. The Bede--Gal derivative, originally introduced for fuzzy and interval-valued functions, is redefined for the set-valued framework and analyzed through its metric properties. Meanwhile, the dH-derivative is formulated in terms of the Pompeiu-Hausdorff metric, allowing differentiability without requiring the existence of the Hukuhara or generalized Hukuhara difference. We establish several results clarifying the relationship between these two concepts, including sufficient conditions under which a function that is Bede-Gal differentiable is also dH-differentiable, and conversely. Illustrative examples are provided to demonstrate cases where one type of differentiability exists while the other fails. The comparison emphasizes that dH-differentiability provides a broader and more flexible framework, extending the applicability of the differential calculus in set-valued analysis.
Co-Authors Wildan Bagus Wicaksono