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On some spaces of lacunary convergent sequences derived by Nörlund-type mean and weighted lacunary statistical convergence. (English) Zbl 1312.46006

Arab J. Math. Sci. 20, No. 2, 250-263 (2014); corrigendum ibid. 22, No. 2, 285 (2016).
Summary: In this paper, we define some new sequence spaces of lacunary convergent sequences derived by Nörlund-type (Riesz) means, which shall be denoted by \(|\overline N,p_r,\theta|\) and \((\overline N,p_r,\theta)\), and investigate some relations between the sequence space \(|\overline N,p_r,\theta|\) with the spaces \(| w_\theta|\) and \(|\overline N,p_n|\). Further, we define a new concept, named weighted lacunary statistical convergence, and examine some connections between this notion and the concept of lacunary statistical convergence and weighted statistical convergence. Also, some topological properties of these new sequence spaces are investigated.

MSC:

46A45 Sequence spaces (including Köthe sequence spaces)
40A35 Ideal and statistical convergence
40C05 Matrix methods for summability
40A05 Convergence and divergence of series and sequences
40F05 Absolute and strong summability
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