Year: 2013
Type: article
Abstract: Let $f$ be a function from $\mathbf{R}^p$ to $\mathbf{R}^q$ and let $\Lambda$ be a finite set of pairs $(\theta, \eta) \in \mathbf{R}^p \times \mathbf{R}^q$. Assume that the real-valued function $\langle\eta, f(x)\rangle$ is Lipschitz continuous in the direction $\theta$ for every $(\theta, \eta) \in \Lambda$. Necessary and sufficient conditions on $\Lambda$ are given for this assumption to imply each of the following: (1) that $f$ is Lipschitz continuous, and (2) that $f$ is continuous with modulus of continuity $\le C\epsilon |{\log \epsilon}|$.
Source: MATHEMATICA SCANDINAVICA
Authors: Dieudonné Agbor, Jan Boman
Institutions: Uppsala University, University of Buea, Stockholm University
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1594928403