Mazur-Ulam theorem in probabilistic normed groups

Document Type : Research Paper


1 Department of Mathematics, Payame Noor University, Tehran, Iran

2 Faculty of Mathematics, K.N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran


In this paper, we give a probabilistic counterpart of  Mazur-Ulam theorem  in probabilistic normed groups. We show, under some conditions, that every surjective isometry between two probabilistic normed groups is a homomorphism.


Volume 8, Issue 2
December 2017
Pages 327-333
  • Receive Date: 23 March 2016
  • Revise Date: 24 October 2016
  • Accept Date: 21 July 2017