Document Type : Research Paper

Authors

• Alireza Pourmoslemi ¹
• Kourosh Nourouzi ²

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

Abstract

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.

Keywords

• Probabilistic normed groups
• Invariant probabilistic metrics
• Mazur-Ulam Theorem