A NOTE ON DIRECTIONAL LIPSCHITZ CONTINUITY IN THE EUCLIDEAN PLANE

David Hruška

doi:10.14321/realanalexch.46.2.0441

Abstract

We prove a stronger version of a conjecture stated in a paper from 2017 by J. M. Ash and S. Catoiu concerning relations between various notions of the Lipschitz property and differentiability in the Euclidean plane. We also provide an improved version of the main result of that paper.

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David Hruška. "A NOTE ON DIRECTIONAL LIPSCHITZ CONTINUITY IN THE EUCLIDEAN PLANE." Real Anal. Exchange 46 (2) 441 - 450, 2021. https://doi.org/10.14321/realanalexch.46.2.0441

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Published: 2021

First available in Project Euclid: 9 November 2021

MathSciNet: MR4336566

Digital Object Identifier: 10.14321/realanalexch.46.2.0441

Subjects:

Primary: 26A03 , 26A04

Secondary: 26A05

Keywords: $\sigma$-porosity , Baire categories , directional Lipschitz continuity , directional smoothness , porosity

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