Local stability of isometries on $ 4 $-dimensional Euclidean spaces

Abstract

<abstract><p>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.</p></abstract>