On some spaces of lacunary convergent sequences derived by Nörlund-type mean and weighted lacunary statistical convergence | Zendy

Metin Başarır | Zendy; Şükran Konca | Zendy

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On some spaces of lacunary convergent sequences derived by Nörlund-type mean and weighted lacunary statistical convergence

Author(s) -

Metin Başarır,

Şükran Konca

Publication year - 2013

Publication title -

arab journal of mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.353

H-Index - 11

eISSN - 2588-9214

pISSN - 1319-5166

DOI - 10.1016/j.ajmsc.2013.09.002

Subject(s) - lacunary function , mathematics , sequence (biology) , convergence (economics) , type (biology) , limit of a sequence , discrete mathematics , weak convergence , pure mathematics , combinatorics , mathematical analysis , ecology , genetics , computer security , limit (mathematics) , computer science , economics , asset (computer security) , biology , economic growth

In this paper, we define some new sequence spaces of lacunary convergent sequences derived by Nörlund-type (Riesz) mean, which shall be denoted by |N‾,pr,θ| and (N‾,pr,θ), and investigate some relations between the sequence space |N‾,pr,θ| with the spaces ∣wθ∣ and |N‾,pn|. Further, we define a new concept, named weighted lacunary statistical convergence and examine some connections between this notion with the concept of lacunary statistical convergence and weighted statistical convergence. Also, some topological properties of these new sequence spaces are investigated

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