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...
moreIn 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.