Comparison of Set-Valued Function Derivatives: Bede-Gal and Hausdorff Versions
Undergraduate thesis, Universitas Brawijaya, 2026
The original Indonesian title is Perbandingan Turunan Fungsi Bernilai Himpunan Versi Bede-Gal dan Hausdorff.
This Indonesian-language undergraduate thesis examines two notions of differentiation for compact convex set-valued functions. It compares the Bede-Gal derivative, which depends on the existence of the Hukuhara difference, with the more flexible Hausdorff derivative formulated through the Pompeiu-Hausdorff metric. The thesis also studies closed interval-valued functions and identifies conditions under which the two derivatives agree.
The main relationship is one-way in general: Bede-Gal differentiability implies Hausdorff differentiability, while the converse requires the relevant Hukuhara differences to exist locally.
This is the public version of the thesis. Personal identifiers and administrative signature pages have been omitted, and an English abstract is included.
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Recommended citation: Wicaksono, Wildan Bagus. Comparison of Set-Valued Function Derivatives: Bede-Gal and Hausdorff Versions. Undergraduate thesis, Universitas Brawijaya, 2026.
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