Strongly (psi)-Bounded and Classes of Linear Operators in Probabilistic Normed Space

In this paper we redefined the definition of a bounded linear operator in probabilistic normed space by introducing the notion of strongly (psi)- bounded linear maps. We then show that this new definition of boundedness implies all contraction functions in probabilistic normed space are bounded. Also, we introduce the classes of linear operators in probabilistic normed space, as the set of all certainly bounded Lc(V, V ), D-bounded LD(V, V ), strongly (psi)-bounded L(psi)(V, V ), and strongly -bounded L (V, V ) we then prove they are linear spaces.