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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 70 Issue: 1

Deferred Nörlund statistical relative uniform convergence and Korovkin-type approximation theorem

Kamil Demirci(Sinop University)0000-0002-5976-9768
Fadime Dirik(SINOP UNIVERSITY)0000-0002-9316-9037
Sevda Yıldız(Sinop Üniversitesi)0000-0002-4730-2271
Pages
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Publication Date
2021-06-30
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Additionally, we estimate the rate of convergence of approximating positive linear operators by means of the modulus of continuity.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper, we define the concept of statistical relative uniform convergence of the deferred Nörlund mean and we prove a general Korovkin-type approximation theorem by using this convergence method.
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Key Findings & Data:As an application, we use classical Bernstein polynomials for defining an operator that satisfies our new approximation theorem but does not satisfy the theorem given before.
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Conclusion & Impact:Additionally, we estimate the rate of convergence of approximating positive linear operators by means of the modulus of continuity.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Statistical convergence · statistical relative uniform convergence · Nörlund summability

Abstract

In this paper, we define the concept of statistical relative uniform convergence of the deferred Nörlund mean and we prove a general Korovkin-type approximation theorem by using this convergence method. As an application, we use classical Bernstein polynomials for defining an operator that satisfies our new approximation theorem but does not satisfy the theorem given before. Additionally, we estimate the rate of convergence of approximating positive linear operators by means of the modulus of continuity.

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Cite This Article

Demirci, K., Dirik, F., Yıldız, S. (2021). Deferred Nörlund statistical relative uniform convergence and Korovkin-type approximation theorem. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 70 Issue: 1. https://doi.org/10.31801/cfsuasmas.807169

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