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<p>In this paper, we introduce some operators based on binomial operators involving Sheffer polynomials, which allows us to approximate continuous functions on unbounded intervals. We investigate the approximation properties of the operators in weighted spaces. With the help of the first and second modulus of continuity, we obtain the degree of approximation of continuous functions using Petree’s <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2970_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\kappa \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>κ</mi> </math></EquationSource> </InlineEquation>-functional. We also find the approximation degree for functions of the modified Lipschitz class. Eventually, according to the choices of the generating function <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2970_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">\(h\left( t\right) \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>h</mi> <mfenced close=")" open="("> <mi>t</mi> </mfenced> </mrow> </math></EquationSource> </InlineEquation>, the operator includes Laguerre-type, Bell-type, and Chlodowsky-type operators in special cases. We illustrate the approximation of these special cases for some functions. Finally, we give the generalization of the operator.</p>

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Approximation with Chlodowsky–Sheffer Operators on Unbounded Intervals

  • 期刊论文

  • 发表日期：

    2025年10月16日

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  • Mehmet Ali Özarslan,
  • Bayram Çekim,
  • Sezin Çit

摘要

In this paper, we introduce some operators based on binomial operators involving Sheffer polynomials, which allows us to approximate continuous functions on unbounded intervals. We investigate the approximation properties of the operators in weighted spaces. With the help of the first and second modulus of continuity, we obtain the degree of approximation of continuous functions using Petree’s \(\kappa \) κ -functional. We also find the approximation degree for functions of the modified Lipschitz class. Eventually, according to the choices of the generating function \(h\left( t\right) \) h t , the operator includes Laguerre-type, Bell-type, and Chlodowsky-type operators in special cases. We illustrate the approximation of these special cases for some functions. Finally, we give the generalization of the operator.