On Normed Space Valued Paranormed Orlicz Space of Bounded Functions and Its Topological Structures

This paper attempts to introduce and study a new class (X, U, , p) of Banach space valued function space using Orlicz function as a generalization of the basic space ofbounded sequences. Besides the investigation of linear topological structures of the class (X, U, , p), our primarily interest is to explore the conditions pertaining to the containment relation between the classes (X, U, , p) in terms of different values of p.