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Journals / Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi / 2026 / Cilt: 42 Sayı: 3

Summability Results for Infinite and Fourier Series

Sonsuz Seriler ve Fourier Serileri için Toplanabilme Sonuçları

Bağdagül Kartal Erdoğan(Erciyes Üniversitesi)0000-0001-6223-0838
Pages
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Publication Date
2026-09-08
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

The findings of this paper contribute to the summability theory of infinite series and demonstrate the usefulness of the proposed method in Fourier analysis.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, a theorem related to a general summability method is proved.
📊
Key Findings & Data:The purpose of the paper is to investigate the fundamental properties of this method and to determine conditions under which it can be effectively applied to series that are not convergent in the usual sense.
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Conclusion & Impact:The findings of this paper contribute to the summability theory of infinite series and demonstrate the usefulness of the proposed method in Fourier analysis.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:toplanabilme çarpanları · fourier serileri · mutlak toplanabilme

Abstract

In this study, a theorem related to a general summability method is proved. The purpose of the paper is to investigate the fundamental properties of this method and to determine conditions under which it can be effectively applied to series that are not convergent in the usual sense. The results obtained provide a broader perspective on summability theory and extend several known results in the literature. As an application of the established theorem, a result concerning the summability of trigonometric Fourier series is derived. In particular, sufficient conditions ensuring the summability of Fourier series are discussed. The findings of this paper contribute to the summability theory of infinite series and demonstrate the usefulness of the proposed method in Fourier analysis.

Özet

Bu çalışmada, genel bir toplanabilme yöntemiyle ilgili bir teorem ispatlanmıştır. Makalenin amacı, bu yöntemin temel özelliklerini incelemek ve klasik anlamda yakınsak olmayan serilere hangi koşullar altında etkili bir şekilde uygulanabileceğini belirlemektir. Elde edilen sonuçlar, toplanabilirlik teorisine daha geniş bir bakış açısı kazandırmakta ve literatürdeki bazı bilinen sonuçları genelleştirmektedir. İspatlanan teoremin bir uygulaması olarak, trigonometrik Fourier serilerinin toplanabilirliği ile ilgili bir sonuç elde edilmiştir. Özellikle Fourier serilerinin toplanabilirliğini garanti eden yeter koşullar ele alınmıştır. Bu çalışmanın bulguları, sonsuz serilerin toplanabilirlik teorisine katkı sağlamakta ve önerilen yöntemin Fourier analizindeki kullanışlılığını ortaya koymaktadır.

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Cite This Article

Erdoğan, B. K. (2026). Summability Results for Infinite and Fourier Series. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi, Cilt: 42 Sayı: 3. https://doi.org/10.65520/erciyesfen.1879948

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