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<p>The current paper discusses some important approximation properties of a new modification of the Phillips operators with the help of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13660_2025_3260_Article_IEq2.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msup> <mi>A</mi> <mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msup> </math></EquationSource> <EquationSource Format="TEX">$A^{(2)}$</EquationSource> </InlineEquation> class Appell polynomials. Firstly, we present the convergence rate of our new operators by using modulus of continuity. Then we establish a quantitative Voronovskaya-type asymptotic result. We also introduce Hermite polynomials and Gould–Hopper polynomials, which are more specific examples of Appell polynomials.</p>

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A generalization of Phillips operators by using the Appell polynomials of class \(A^{(2)}\)

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月5日

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  • Melek Sofyalıoğlu Aksoy

摘要

The current paper discusses some important approximation properties of a new modification of the Phillips operators with the help of A ( 2 ) $A^{(2)}$ class Appell polynomials. Firstly, we present the convergence rate of our new operators by using modulus of continuity. Then we establish a quantitative Voronovskaya-type asymptotic result. We also introduce Hermite polynomials and Gould–Hopper polynomials, which are more specific examples of Appell polynomials.