Local stability of isometries on 4-dimensional Euclidean spaces

Abstract

In 1982, Fickett attempted to prove the Hyers-Ulam stability of isometries defined on a bounded subset of $ \mathbb{R}^n $. In this paper, we applied an intuitive and efficient approach to prove the Hyers-Ulam stability of isometries defined on the bounded subset of $ \mathbb{R}^4 $, and we significantly improved Fickett's theorem for the four-dimensional case.

Keywords

• isometry
• $ \varepsilon $-isometry
• hyers-ulam stability
• fickett's theorem