Some new classes of paranorm ideal convergent double sequences of sigma-bounded variation over n-normed spaces

摘要

AbstractThe sequence space BVσ, the space of all sequence of σ-bounded variation, was firstly defined and studied by Mursaleen. Later on, Vakeel and Tabassum developed the same space to double sequences. Recently, using the concept of I-convergence, Vakeel and Vakeel et al. and others introduced many sequence spaces related to the space we just mentioned above which are defined by different operators. In this article, we keep the same direction up introducing some new classes of I-convergent double sequences of σ-bounded variation over n-normed spaces. In addition, we study some basic topological and algebraic properties of these classes. Also, we prove some inclusion relations on these classes.