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.