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<p>In this paper, we modify the classical Kantorovich operators, very well known in Approximation Theory, by considering <i>p</i>-averages (whose expressions are of the form of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^p\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation> (quasi-)norms, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(p&gt;0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>). We establish convergence results, an asymptotic formula covering the general setting; moreover, we show that, under suitable assumptions, our operators perform better than the classical Kantorovich ones in approximating functions. Because of the nature of the <i>p</i>-averages, the proposed operators are nonlinear, so their study turns out to be more challenging.</p>

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A nonlinear version of Kantorovich operators with p-averages: convergence results and asymptotic formula

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月3日

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  • Mirella Cappelletti Montano,
  • Rosario Corso,
  • Vita Leonessa

摘要

In this paper, we modify the classical Kantorovich operators, very well known in Approximation Theory, by considering p-averages (whose expressions are of the form of \(L^p\) L p (quasi-)norms, \(p>0\) p > 0 ). We establish convergence results, an asymptotic formula covering the general setting; moreover, we show that, under suitable assumptions, our operators perform better than the classical Kantorovich ones in approximating functions. Because of the nature of the p-averages, the proposed operators are nonlinear, so their study turns out to be more challenging.