The Specular Derivative
Classical Analysis and ODEs
2025-12-30 v2
Abstract
In this paper, we introduce a new generalized derivative, which we term the specular derivative. We establish the Quasi-Rolles' Theorem, the Quasi-Mean Value Theorem, and the Fundamental Theorem of Calculus in light of the specular derivative. We also investigate various analytic and geometric properties of specular derivatives and apply these properties to several differential equations.
Cite
@article{arxiv.2210.06062,
title = {The Specular Derivative},
author = {Kiyuob Jung and Jehan Oh},
journal= {arXiv preprint arXiv:2210.06062},
year = {2025}
}
Comments
34 pages, 11 figures