On the improvement of Fickett's theorem on bounded sets

Abstract

Fickett proved the stability of isometries on bounded subsets of R-n for n >= 2. Jung then improved Fickett's theorem for n >= 3. In this paper, we improve Fickett's theorem for n = 2 and improve Jung's result for n = 3, by employing a fundamental analytic method, as it can be used to explain mathematically many practical engineering problems.