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<p>In this paper, we introduce a new type of modified Bernstein-Kantorovich operators in movable interval, which reproduce affine functions. We obtain a Jackson type theorem with Ditzian-Totik type modulus of smoothness for approximation of continuous functions, and a Voronovskaja type asymptotic estimate for approximation of smooth functions.</p>

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On Bernstein-Kantorovich Operators reproducing affine functions in movable interval

  • 期刊论文

  • 发表日期：

    2025年9月2日

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  • Jiang Bing,
  • Yu Dansheng

摘要

In this paper, we introduce a new type of modified Bernstein-Kantorovich operators in movable interval, which reproduce affine functions. We obtain a Jackson type theorem with Ditzian-Totik type modulus of smoothness for approximation of continuous functions, and a Voronovskaja type asymptotic estimate for approximation of smooth functions.