Hyers-Ulam stability of isometries on bounded domains-II

Abstract The question of whether there is a true isometry approximating the ε \varepsilon -isometry defined in the bounded subset of the n n -dimensional Euclidean space has long been considered an interesting question. In 1982, Fickett published the first article on this topic, and in early 2000, Alestalo et al. and Väisälä improved Fickett’s result significantly. Recently, the second author of this article published a paper improving the previous results. The main purpose of this article is to significantly improve all of the aforementioned results by applying a basic and intuitive method.