(A)(C, β) toplanabilme metodu için Tauber tipi teoremler

Abstract

Bu çalışmada, Abel toplanabilirlik yöntemi için klasik Tauber teoremlerini genişleten iki Tauber tipi teorem incelenmektedir. Bu teoremlerin amacı, bir dizinin (C, α) toplanabilirliğini, Abel ve Cesàro toplanabilirlik yöntemlerinin β mertebeden çarpımından elde etmektir; burada β>α>-1 ve α, β ∈ R'dir. β>α=0 özel durumunda, (A)(C, β) toplanabilirlikten yakınsamaya geçiş için bir koşul verilmiştir. Bu sonuçlar, yalnızca mevcut Tauber tipi teoremleri genellemekle kalmaz, aynı zamanda Abel ve Cesàro toplanabilirlik yöntemleri arasındaki etkileşime yeni bir bakış açısı sunar. Ayrıca, bu teoremler, dizi analizinde toplanabilirlik tekniklerinin ve matematiksel serilerdeki uygulamalarının daha geniş bir anlayışına katkıda bulunmaktadır.

Keywords

• (A)(C, $\alpha$) toplanabilme
• (C, $\alpha$) toplanabilme
• Abel toplanabilme
• Tauber tipi teoremler

Ethical Statement

Bu çalışmada bilimsel etik kurallara uyulduğunu, çıkar çatışmasının bulunmadığını ve çalışmanın başka bir dergiye gönderilmediğini beyan ederim.

Tauberian theorems for the (A)(C, β) summability methods

Abstract

In this study, we investigate two Tauberian theorems that extend the classical Tauberian theorems for the Abel summability method. The aim of these theorems is to derive the (C, α) summability of a sequence from the product of its Abel and Cesàro summability methods of order β, where β>α>-1 and α,β∈R. In the special case where β>α=0, a condition is provided for the transition from (A)(C, β) summability to convergence. These results not only generalize existing Tauberian theorems but also offer new insights into the interplay between Abel and Cesàro summability methods. Furthermore, the theorems contribute to the broader understanding of summability techniques in sequence analysis and their applications in mathematical series.

Keywords

• (A)(C, $\alpha$) summability
• (C, $\alpha$) summability
• Abel summability
• Tauberian theorems

Ethical Statement

I declare that this study complies with scientific ethical standards, contains no conflict of interest, and has not been submitted to another journal.

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