On Locally Convex Topological Vector Space Valued Paranormed Function Space Defined by Orlicz Function

Abstract

The aim of this paper is to introduce and study a new class (l_∞ (X, Y, Φ, ξ, w , L), H_U) of locally convex space Y- valued functions using Orlicz function Φ as a generalization of some of the well known sequence spaces and function spaces. Besides the investigation pertaining to the linear topological structures of the class (l_∞ (X, Y, Φ, ξ, w , L), H_U) when topologized it with suitable natural paranorm , our primarily interest is to explore the conditions pertaining the containment relation of the class l_∞ (X, Y, Φ, ξ, w) in terms of different ξ and w so that such a class of functions is contained in or equal to another class of similar nature.

DOI: http://dx.doi.org/10.3126/njst.v14i2.10423  

Nepal Journal of Science and Technology Vol. 14, No. 2 (2013) 109-116