A Tauberian theorem for the logarithmic summability in ordered spaces

Abstract

The present manuscript aims to extend a Tauberian theorem previously established for the Cesàro and weighted mean summability methods of single sequences in ordered spaces to the logarithmic summability method, also known as the (ℓ,1,1) method, for double sequences. In order to achieve this, we present several Tauberian conditions which address the O_L-oscillatory behavior of a double sequence (s_mn ) with respect to logarithmic summability in certain senses. These conditions facilitate the transition from (ℓ,1,1), (ℓ,1,0), and (ℓ,0,1) summability to P-convergence in ordered spaces.

Keywords

• Double sequences
• ordered linear spaces
• slowly decreasing sequences with respect to (l,1,1)
• Tauberian conditions
• Tauberian theorems
• logarithmic summability method

Sıralı uzaylarda logaritmik toplanabilme için bir Tauber tipi teorem

Abstract

Bu çalışma daha önce sıralı uzaylardaki tek katlı dizilerin Cesàro ve ağırlıklı ortalama toplanabilirlik yöntemleri için oluşturulmuş Tauber tipi teoremleri, iki katlı diziler için logaritmik toplanabilirlik yöntemine, diğer adıyla (ℓ,1,1) yöntemine genişletmeyi amaçlar. Bu amaçla, çeşitli anlamlarda logaritmik toplanabilirliğe göre iki katlı bir (s_mn ) dizinin O_L-salınım davranışını ele alan birkaç Tauber tipi koşul sunuyoruz. Bu koşullar, sıralı uzaylarda dizinin (ℓ,1,1), (ℓ,1,0) ve (ℓ,0,1) toplanabilirliğinden P-yakınsaklığına geçişine olanak sağlar.

Keywords

• Çift diziler
• sıralı doğrusal uzaylar
• (l,1,1) metoduna göre yavaş azalan diziler
• Tauber koşullar
• Tauber teoremler
• logaritmik toplanabilme metodu

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