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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 71 Issue: 2

Approximation by Szasz-Mirakjan-Durrmeyer operators based on shape parameter $\lambda$

Reşat Aslan(Çalışma ve İş kurumu)0000-0002-8180-9199
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Publication Date
2022-06-30
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Finally, we give the comparison of the convergence of these newly defined operators to the certain functions with some graphics and error of approximation table.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we study several approximation properties of Szasz-Mirakjan-Durrmeyer operators with shape parameter λ ∈ [ − 1 , 1 ] λ∈[−1,1] .
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Key Findings & Data:Firstly, we obtain some preliminaries results such as moments and central moments.
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Conclusion & Impact:Finally, we give the comparison of the convergence of these newly defined operators to the certain functions with some graphics and error of approximation table.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Modulus of continuity · Lipschitz type class · Voronovskaya type asymptotic theorem

Abstract

In this paper, we study several approximation properties of Szasz-Mirakjan-Durrmeyer operators with shape parameter λ ∈ [ − 1 , 1 ] λ∈[−1,1] . Firstly, we obtain some preliminaries results such as moments and central moments. Next, we estimate the order of convergence in terms of the usual modulus of continuity, for the functions belong to Lipschitz type class and Peetre's K-functional, respectively. Also, we prove a Korovkin type approximation theorem on weighted spaces and derive a Voronovskaya type asymptotic theorem for these operators. Finally, we give the comparison of the convergence of these newly defined operators to the certain functions with some graphics and error of approximation table.

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Cite This Article

Aslan, R. (2022). Approximation by Szasz-Mirakjan-Durrmeyer operators based on shape parameter $\lambda$. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 71 Issue: 2. https://doi.org/10.31801/cfsuasmas.941919

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