On Certain Linear Structure of Orlicz Space c0 (M, (X, ||.||), ā, ᾱ) of Vector Valued Difference Sequence

Abstract

In this article, we introduce and study a new class c0 (M, (X, ||.||), ā, ᾱ) of normed space (X, ||.||) valued difference sequences with the help of Orlicz function M . This is a generalization of the classical sequence space c0. Our primary interest is to explore some linear structures and investigate the conditions relating to the containment relation of the class c0 (M, (X, ||.||), ā, ᾱ) in terms of different ā and ᾱ.

On I-Convergence Difference Sequence Spaces Defined by Orlicz Function in 2−Normed Space

“…The notion of ideal convergence was introduced as a generalization of statistical convergence, first by Kostyrko et al [8]. For more details about these types of sequence spaces, one may refer to Dutta [1], Ghimire [3], Ghimire and Pahari [4,5], Hazarika et al [6], Mursaleen and Alotaibi [11], Mursaleen and Mohiduddine [12], Mursaleen and Sharma [13], Sahiner et al [15], Salat et al [16], Savas and Gurdal [17], Savas [18,19], Tripathy and Hazarika [20] and many others. Definition 1.6.…”

On Topological Structure of Total Paranormed Double Sequence Space (ℓ 2 ((X, ||.||), γ, ¯ w¯), G)

“…The concept of paranorm is closely related to the linear metric space; see Wilansky [26] and its studies on sequence spaces were initiated by Maddox [9], and many others. Basarir and Altundag [1], Ghimire, & Pahari [2,3], Parasar and Choudhary [15], Paudel and Pahari [18,20,21] and many others further studied the various types of paranormed sequence spaces.…”