Hyers-Ulam stability of isometries on bounded domains

Abstract

More than 20 years after Fickett attempted to prove the Hyers-Ulam stability of isometries defined on bounded subsets of ${\mathbb{R}}^n$ in 1981, Väisälä improved Fickett's result significantly. In this paper, we will improve Fickett's theorem by proving the Hyers-Ulam stability of isometries defined on bounded subsets of ${\mathbb{R}}^n$ using a more intuitive method different from that used by Väisälä.

arXiv comment17 pages