On Banach Space Valued Orlicz Function Space l (X, U, ||.||, ξ ) and its Generalized Form l (X, U, ||.||, ξ, λ, p)

Abstract

This paper attempts to introduce and study a new class l (X, U, ||.||, ξ ) and its generalized form l (X, U, ||.||, ξ, λ, p) of Normed space valued function space using Orlicz function ξ as the generalizations of the basic sequence space l.  Besides the investigation of linear topological structures of the class l (X, U, ||.||, ξ ) when topologized it with suitable natural norm, our primarily interest is to explore the conditions pertaining to the containment relation between the classes l (X, U, ||.||, ξ, λ, p) in terms of different values of λ and p.