paper

A Note on an Approximate Fixed Point Theorem for Maps

arXiv:2606.15670

Abstract

We prove an approximate fixed point theorem for maps of vanishing mean oscillation from the unit ball to itself. This gives a short proof of the Open Problem 5.10 of Brezis [Rend. Lincei Mat. Appl. 34 (2023), 307--335].

8 pages. A short self-contained proof of Brezis' Open Problem 5.10. Comments are welcome!

A Note on an Approximate Fixed Point Theorem for $\operatorname{VMO}$ Maps · wovepaper