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<p>In the present article, we study the approximation properties of constructed operators based on the shape parameter <i>α</i>. We construct the Stancu-type operators of <i>α</i>-Bernstein–Schurer–Kantorovich operators. Here the shape parameter <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13660_2025_3293_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="66" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>α</mi> <mo>∈</mo> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">]</mo> </math></EquationSource> <EquationSource Format="TEX">$\alpha \in [0,1]$</EquationSource> </InlineEquation>. We obtain the convergence of proposed operators in terms of Lipschitz-continuous functions and Peetre’s <i>K</i>-functional by using the modulus of continuity of orders one and two.</p>

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Approximation by Stancu-type α-Bernstein-Schurer-Kantorovich operators

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  • 发表日期：

    2025年4月8日

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  • Md. Nasiruzzaman

摘要

In the present article, we study the approximation properties of constructed operators based on the shape parameter α. We construct the Stancu-type operators of α-Bernstein–Schurer–Kantorovich operators. Here the shape parameter α ∈ [ 0 , 1 ] $\alpha \in [0,1]$ . We obtain the convergence of proposed operators in terms of Lipschitz-continuous functions and Peetre’s K-functional by using the modulus of continuity of orders one and two.