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

Cogent Mathematics & Statistics

Vakeel A. Khan¹  Kamal M.A.S. Alshlool¹  Sameera A.A. Abdullah¹  Rami K.A. Rababah²  Ayaz Ahmad³ 

[1] Aligarh Muslim University;Amman Arab University;National Institute of Technology;

关键词: invariant mean;    sequence of $ \sigma $-bounded variation;    n-normed space;    paranormed space;    orlicz function;    ideal;    filter;    i-convergence double sequence over n-normed space;    i-null over n-normed space;    i-cauchy over n-normed space;    i-bounded over n-normed space;    solid space;    sequence algebra;    convergence free space;   

DOI  :  10.1080/25742558.2018.1460029

来源: DOAJ

【 摘 要 】

The sequence space $ BV_{\sigma } $, the space of all sequence of $ \sigma $-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 $ \sigma $-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.

【 授权许可】

Unknown