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Journals / Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi / 2026 / Volume: 16 Issue: 1

On Asymptotically Lacunary Statistically ɸ-Equivalent Triple Sequences

Asimptotik Lacunary İstatistiksel ɸ-Denk Üç İndisli Diziler

Mualla Birgül Huban(ISUBU, Büyükkutlu Uygulamalı Bilimler Fakültesi)0000-0003-2710-8487
Pages
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Publication Date
2021-05-27
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Also, the relationship between these new notations will be given.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The concept of statistical convergence was first given by Fast [2].
📊
Key Findings & Data:Marouf [13] gave new concepts in asymptotic equivalent series in 1993.
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Conclusion & Impact:Also, the relationship between these new notations will be given.
🔬Design:Research Article
📍Scope:2006 Verileri
⚙️Variables:Triple sequences · Orlicz function · Lacunary Sequence

Abstract

The concept of statistical convergence was first given by Fast [2]. This concept plays an important role in both applied mathematics and other diciplines that include mathematics. Marouf [13] gave new concepts in asymptotic equivalent series in 1993. In his study in 1980, Patterson [16] presented statistical similarities for asymptotic equivalent sequences. In 2006, Patterson and Savaş [17] add a new dimension to these concepts by using the lacunary series. On the other hand, the concept of statistical convergence for triple sequences is presented by Şahiner et al. in study [20]. Also, in some studies in the literature, the statistical convergence of any real series is determined by absolute value. The absolute value of real numbers is known as a special Orlicz function [19]. The primary goal of this article is to introduce the concepts of asymptotically statistically ϕ-equivalent and asymptotically lacunary statistically ϕ-equivalent triple sequences. Using the Orlicz function under special condition, new proofs are given and new concepts are introduced into the literature. Also, the relationship between these new notations will be given.

Özet

İstatistiksel yakınsaklık kavramı ilk kez, Fast [2] tarafından verilmiştir. Bu kavram, hem uygulamalı matematikte hem de matematiği içeren diğer bilim dallarında önemli rol oynar. Marouf [13] ise 1993’te asimptotik denk dizilerde yeni kavramlar vermiştir. 1980’de yaptığı çalışmada ise Patterson [16] asimptotik denk diziler için istatistiksel benzerlerini sunmuştur. 2006’da Patterson ve Savaş [17] lacunary dizileri kullanarak bu kavramlara yeni bir boyut kazandırmıştır. Diğer taraftan, üç indisli diziler için istatistiksel yakınsaklık kavramı Şahiner vd. [20] tarafından sunulmuştur. Aynı zamanda literatürdeki bazı çalışmalarda, herhangi bir reel dizinin istatistiksel yakınsaklığı mutlak değere göre belirlenir. Reel sayıların mutlak değeri özel bir Orlicz fonksiyonu olarak bilinir [19]. Bu makalenin temel amacı, üç indisli diziler için asimptotik olarak istatistiksel ϕ-denk ve asimptotik olarak lacunary istatistiksel ϕ-denk kavramlarını tanımlamaktır. Belli özel koşul altında Orlicz fonksiyonundan yararlanarak, yeni ispatlar vermek ve yeni kavramları literatüre kazandırmaya çalışmaktır. Ayrıca bu yeni notasyonlar arasındaki ilişkiler de çalışmamızda verilmiştir.

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Cite This Article

Huban, M. B. (2021). On Asymptotically Lacunary Statistically ɸ-Equivalent Triple Sequences. Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi, Volume: 16 Issue: 1. https://doi.org/10.29233/sdufeffd.866055

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