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<p>The main idea of this paper is to obtain approximation results by utilizing the shifted knots properties of the family of <i>α</i>-Bernstein operators. We examine some basic results and estimate the moments of this new family of <i>α</i>-Bernstein operators. We derive an upper bound on the error estimation using the usual modulus of continuity in continuous function spaces. Furthermore, we have also obtained the shape-preserving properties and discussed some direct theorems.</p>

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Shape preserving approximation properties to family of α-Bernstein shifted knot operators

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月26日

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  • Mohammad Ayman-Mursaleen,
  • Esmail Alshaban,
  • Md. Nasiruzzaman

摘要

The main idea of this paper is to obtain approximation results by utilizing the shifted knots properties of the family of α-Bernstein operators. We examine some basic results and estimate the moments of this new family of α-Bernstein operators. We derive an upper bound on the error estimation using the usual modulus of continuity in continuous function spaces. Furthermore, we have also obtained the shape-preserving properties and discussed some direct theorems.