On Certain Topological Structures of Normed Space Valued Generalized Orlicz Function Space

Narayan Prasad Pahari

Abstract: The aim of this paper is to introduce and study a new class ?? (S, (T, ||. ||), ?, u) of normed space valued function space using Orlicz function ? as a generalization of well known basic bounded sequence space ????studied in functional analysis. Besides the investigation of linear space structure of the class ?? (S, (T, ||. ||), ?, u), our primarily interest is to explore the conditions pertaining to the containment relation of the class ?? (S, (T, ||. ||), ?, u) in terms of different values of u??

Keywords: Orlicz function, Orlicz Space, Normed Space, Solid space