Hyers-Ulam-Rassias stability of isometries on restricted domains

Abstract

In this paper, the Hyers-Ulam-Rassias stability of isometries on restricted domains will be proved. In section 2, the Hyers-Ulam-Rassias stability of isometries on unbounded (restricted) domains will be proved by using the direct method. This result will be sharpened under some simplified situation by using a similar method presented in [8]. The Hyers-Ulam-Rassias stability problems of isometries on bounded domains will be investigated in section 3.