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Journals / Sinop Üniversitesi Fen Bilimleri Dergisi / 2022 / Cilt: 7 Sayı: 2

Approximation on Modular Spaces via P-Statistical Relative A-Summation Process

Modüler Uzaylar Üzerinde P-İstatistiksel A-Toplam Süreci Aracılığıyla Yaklaşım

Kamil Demirci(SİNOP ÜNİVERSİTESİ)0000-0002-5976-9768
Sevda Yıldız(Sinop Üniversitesi)0000-0002-4730-2271
Pages
152–172
Publication Date
2022-12-30
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AI Summary & Key Takeaways

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

We end the paper with giving some concluding remarks.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we first present the notions of statistical relative modular and F-norm convergence concerning the power series method.
📊
Key Findings & Data:Moreover, we present some estimates of rates of convergence via modulus of continuity.
💡
Conclusion & Impact:We end the paper with giving some concluding remarks.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Korovkin teoremi · modüler uzay · istatistiksel yakınsaklık

Abstract

In this paper, we first present the notions of statistical relative modular and F-norm convergence concerning the power series method. Then, we also present theorems of Korovkin-type via statistical relative A-summation process via power series method on modular spaces, including as particular cases weighted spaces, certain interpolation spaces, Orlicz and Musielak-Orlicz spaces, Lp spaces and many others. Later, we consider some application to Kantorovich-type operators in Orlicz spaces. Moreover, we present some estimates of rates of convergence via modulus of continuity. We end the paper with giving some concluding remarks.

Özet

Bu çalışmada, ilk olarak, kuvvet serisi yöntemiyle ilgili istatistiksel relative modüler ve F-norm yakınsama kavramlarını sunuyoruz. Daha sonra, özel durumlar olarak ağırlıklı uzaylar, belirli enterpolasyon uzayları, Orlicz ve Musielak-Orlicz uzayları, Lp uzayları ve diğer birçok uzayları içeren modüler uzaylar üzerinde kuvvet serisi yöntemiyle istatistiksel relative A-toplam süreci aracılığıyla Korovkin-tipi teoremleri de sunuyoruz. Daha sonra, Orlicz uzaylarında Kantorovich tipi operatörlere bazı uygulamaları göz önüne alıyoruz. Dahası, süreklilik modülü aracılığıyla yakınsama oranlarının bazı tahminlerini sunuyoruz. Makaleyi bazı son sözler vererek bitiriyoruz.

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Cite This Article

Demirci, K., Yıldız, S. (2022). Approximation on Modular Spaces via P-Statistical Relative A-Summation Process. Sinop Üniversitesi Fen Bilimleri Dergisi, Cilt: 7 Sayı: 2, 152–172. https://doi.org/10.33484/sinopfbd.1197502

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