On Locally Convex Topological Vector Space Valued Null Function Space c₀ Defined by Semi Norm and Orlicz Function

Abstract

The aim of this paper is to introduce and study a new class c0 (S, T, Phi, Xi, u) of locally convex space T- valued functions using Orlicz function Phi as a generalization of some of the well known sequence spaces and function spaces. Besides the investigation pertaining to the structures of the class c0 (S, T, Phi, Xi, u), our primarily interest is to explore some of the containment relations of the class c0 (S, T, Phi, Xi, u) in terms of different Xi and u so that such a class of functions is contained in or equal to another class of similar nature.Journal of Institute of Science and Technology, 2014, 19(1): 62-68