Probabilistic Normed Groups

Document Type: Research Paper


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

2 Department of Mathematics, Payame Noor University, P.O.BOX 19395-3697, Tehran, Iran.


In this paper, we introduce the  probabilistic normed groups. Among other results, we investigate the continuity
of inner automorphisms of a group and the continuity of left and right shifts in probabilistic group-norm. We also
 study midconvex functions defined  on probabilistic normed groups and  give  some results about locally boundedness of such  functions.


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