𝛂 Mertebesinde İstatatistiksel Yakınsaklık ve Sınırlılık

Abstract

Bu makalede, terimleri sıfırdan farklı u ve v sayı dizileri için (∆_v^m )_u-istatistiksel yakınsaklık ve (∆_v^m )_u-istatistiksel sınırlılık kavramlarını tanımladık. Daha sonra bu kavramları λ_1=1, λ_(n+1)≤λ_n+1 ve λ_n→∞ (n→∞) şartını sağlayan (λ_n) dizilerini kullanarak (∆_(λ,v)^m )_u-istatistiksel yakınsaklık ve (∆_(λ,v)^m )_u-istatistiksel sınırlılık kavramlarına genişlettik. Daha sonra (∆_(λ,v)^m )_u-istatistiksel yakınsaklık ve (∆_(λ,v)^m )_u-istatistiksel sınırlılık kavramlarını kullanarak 0<α≤1 şartını sağlayan α sayıları yardımıyla (∆_(λ,v)^m )_u (S_c^α) ve (∆_(λ,v)^m )_u (S_b^α) dizi uzaylarını tanımladık. Ayrıca bu dizi uzayları arasındaki ve bazı özel durumlarında elde edilen dizi uzayları arasındaki kapsama bağıntılarını inceledik.

Keywords

• Fark Dizileri
• İstatistiksel Sınırlılık
• İstatistiksel Yakınsaklık

(∆_v^m )_u-Statistical Boundedness and Convergence of Order 𝛂

Abstract

In this paper, we defined the concepts of (∆_v^m )_u-statistical convergence and (∆_v^m )_u-statistical boundedness for sequences u and v with nonzero terms. Then, we extend these concepts to the concepts of (∆_(λ,v)^m )_u-statistical convergence and (∆_(λ,v)^m )_u-statistical boundedness using the sequences (λ_n) satisfying the conditions λ_1=1, λ_(n+1)≤λ_n+1 and λ_n→∞ (n→∞). Then, using the concepts of (∆_(λ,v)^m )_u-statistical convergence and (∆_(λ,v)^m )_u-statistical boundedness, we defined the sequence spaces (∆_(λ,v)^m )_u (S_c^α) and (∆_(λ,v)^m )_u (S_b^α) with the help of numbers α satisfying the condition 0<α≤1. We also investigated the inclusion relations between these sequence spaces and between the sequence spaces obtained in some special cases.

Keywords

• Difference sequences
• Statistical Boundedness
• Statistical Convergence

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