Orlicz difference sequence spaces generated by infinite matrices and de la Vallée-Poussin mean of order α

In this paper we introduce the spaces V^λ[A,M,Δ,p]o,V^λ[A,M,Δ,p] and V^λ[A,M,Δ,p]∞ generated by infinite matrices defined by Orlicz functions. Also we introduce the concept of S^λ[A,Δ]−convergence and derive some results between the spaces S^λ[A,Δ] and V^λ[A,Δ]. Further, we study some geometrical pr...

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Published in:Journal of the Egyptian Mathematical Society 2016-10, Vol.24 (4), p.545-554
Main Authors: Hazarika, Bipan, Esi, Ayhan, Esi, Ayten, Tamang, Karan
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Language:English
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Infinite matrix
Orlicz function
Statistical convergence
λ-sequence
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Esi, Ayhan
Esi, Ayten
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description In this paper we introduce the spaces V^λ[A,M,Δ,p]o,V^λ[A,M,Δ,p] and V^λ[A,M,Δ,p]∞ generated by infinite matrices defined by Orlicz functions. Also we introduce the concept of S^λ[A,Δ]−convergence and derive some results between the spaces S^λ[A,Δ] and V^λ[A,Δ]. Further, we study some geometrical properties such as order continuity, the Fatou property and the Banach–Saks property of the new space V^λα[A,Δ,p]∞. Finally, we introduce the notion of almost λ-statistically-[A, Δ]-convergence of order α or S^λα[A,Δ]−convergence and obtain some inclusion relations between the set S^λα[A,Δ] and the space V^λα[A,Δ,p]∞.
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subjects Infinite matrix
Orlicz function
Statistical convergence
λ-sequence
title Orlicz difference sequence spaces generated by infinite matrices and de la Vallée-Poussin mean of order α
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