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Bibliographic Details
Main Author: Jung, Kiyuob
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2601.10950
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author Jung, Kiyuob
author_facet Jung, Kiyuob
contents This paper introduces specular differentiation, which generalizes Gâteaux and Fréchet 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 Fréchet subdifferential of a convex function through specular differentiation.
format Preprint
id arxiv_https___arxiv_org_abs_2601_10950
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Specular differentiation in normed vector spaces: Quasi-Mean Value and Quasi-Fermat Theorems
Jung, Kiyuob
Optimization and Control
Numerical Analysis
Classical Analysis and ODEs
46G05, 46T20, 49J52
This paper introduces specular differentiation, which generalizes Gâteaux and Fréchet 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 Fréchet subdifferential of a convex function through specular differentiation.
title Specular differentiation in normed vector spaces: Quasi-Mean Value and Quasi-Fermat Theorems
topic Optimization and Control
Numerical Analysis
Classical Analysis and ODEs
46G05, 46T20, 49J52
url https://arxiv.org/abs/2601.10950