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<p>In this paper, we construct a Durrmeyer type modification of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\alpha\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-Bernstein operators based upon Pölya distribution. For these newly defined operators, we establish an approximation theorem by means of Bohman–Korovkin’s theorem and analyze the rate of convergence by using modulus of continuity and Lipschitz-type space. To study the asymptotic behaviour of our operators, we estimate Voronovskaya type theorem and Grüss Voronovskaya type theorem. Finally, with the help of a graph generated using Maple, we show the convergence of our operators to certain functions.</p>

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Approximation by \(\alpha\)-Bernstein–Durrmeyer Type Operators Based on Pölya Distribution

  • 期刊论文

  • 发表日期：

    2025年6月11日

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  • Priya Sehrawat,
  • Arun Kajla

摘要

In this paper, we construct a Durrmeyer type modification of \(\alpha\) α -Bernstein operators based upon Pölya distribution. For these newly defined operators, we establish an approximation theorem by means of Bohman–Korovkin’s theorem and analyze the rate of convergence by using modulus of continuity and Lipschitz-type space. To study the asymptotic behaviour of our operators, we estimate Voronovskaya type theorem and Grüss Voronovskaya type theorem. Finally, with the help of a graph generated using Maple, we show the convergence of our operators to certain functions.