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arXiv · 2601.10950

Specular differentiation in normed vector spaces: Quasi-Mean Value and Quasi-Fermat Theorems

Kiyuob Jung
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Abstract

This paper introduces specular differentiation, which generalizes G\^ateaux and Fr\'echet differentiation in normed vector spaces. We investigate its fundamental theoretical properties and establish weak forms of the Mean Value Theorem and Fermat's Theorem in the specular sense. Finally, we identify a distinguished element of the Fr\'echet subdifferential of a convex function through specular differentiation.

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Kiyuob Jung. 2026-01-16. Specular differentiation in normed vector spaces: Quasi-Mean Value and Quasi-Fermat Theorems. https://arxiv.org/abs/2601.10950

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