On Certain Topological Structures of Summable Paranormed Sequence Space Defined in Two - Normed Space

Abstract

The aim of this paper is to introduce and study a new class  (S, -, u -) of sequences with values in 2-Banach space as a generalization of the familiar space of summable sequences  . We explore some of the preliminary results that characterize the topological linear structure of  the class  (S, -, u -) when topologized it with suitable natural paranorm.