Volume 28 • Number 2 • 2005   • Strongly ψ-Bounded and Classes of Linear Operators in Probabilistic Normed Space Iqbal Hamzh Jebril and Mohd. Salmi Md. Noorani Abstract. In this paper we redefined the definition of a bounded linear operator in probabilistic normed space by introducing the notion of strongly ψ-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 B-bounded LB(V,V'), and strongly ψ-bounded Lψ(V,V') we then prove they are linear spaces. 2000 Mathematics Subject Classification: 54E70. Full text: PDF