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Journals / Turkish Journal of Mathematics and Computer Science / 2024 / Volume: 16 Issue: 2

A Note on Approximation Properties of Bernstein-type Operators via Some Summability Methods

Dilek Soylemez Ozden(SELÇUK ÜNİVERSİTESİ, FEN FAKÜLTESİ)0000-0002-6802-8064
Emre Güven(SELCUK UNIVERSITY)0000-0002-6000-8077
Pages
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Publication Date
2024-12-31
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

We support our results with an example and a graph.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper, we focus on two summability methods and investigate some applications of them for the Cheney-Sharma operators.
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Key Findings & Data:We also analyze the convergence rates employing both the modulus of continuity and elements of the Lipschitz class.
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Conclusion & Impact:We support our results with an example and a graph.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Cheney-Sharma operators · power series statistical convergence · rate of convergence

Abstract

In this paper, we focus on two summability methods and investigate some applications of them for the Cheney-Sharma operators. We obtain approximation properties of the Cheney-Sharma operators via power series statistical convergence. We also analyze the convergence rates employing both the modulus of continuity and elements of the Lipschitz class. Additionally, we define r-th order generalization of the these operators which is linear but don't satisfy the positivity property and investigate approximation properties of these operators, via A-statistical convergence. We support our results with an example and a graph.

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Cite This Article

Ozden, D. S., Güven, E. (2024). A Note on Approximation Properties of Bernstein-type Operators via Some Summability Methods. Turkish Journal of Mathematics and Computer Science, Volume: 16 Issue: 2. https://doi.org/10.47000/tjmcs.1410387

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