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Some new \(I\)-convergent double sequences space of invariant means. (English) Zbl 1348.46006
Summary: The double sequence space \(_2BV_\sigma\) was introduced by V. A. Khan and S. Tabassum [Commun. Fac. Sci. Univ. Ank., Sér. A1, Math. Stat. 60, No. 2, 11–21 (2011; Zbl 1281.46006)] as an interesting generalization of \(BV_\sigma\) introduced by Mursaleen [Q. J. Math., Oxf. II. Ser. 34, 77–86 (1983; Zbl 0539.40006)]. In this paper we define \(_2BV_\sigma^I(p)\) where \(p=(p_{jk})\) a sequence of positive real numbers using the notion of ideals in double sequence spaces. Further we study the topological properties and some inclusion relations on this space.
MSC:
46A45 Sequence spaces (including Köthe sequence spaces)
40A35 Ideal and statistical convergence
40B05 Multiple sequences and series (should also be assigned at least one other classification number in this section)
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