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This paper furthers the study of the operators \(M_{n,j,\nu }\) , which preserve the functions 1 and \(x^j\) and reduce to the genuine Bernstein-Durrmeyer operators when \(j=\nu =1\) . The focus is on key properties of these operators, particularly examining their moments and the rate of convergence in terms of the modulus of continuity. Additionally, new results are provided regarding the behavior of \(M_{n,j,\nu }\) with respect to \(\{1, x^j\}\) -convex functions and the operators’ shape-preserving properties.

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Genuine Bernstein-Durrmeyer Type Operators Preserving 1 and \(x^j\) (II)

  • 会议论文

  • 发表日期：

    2026年

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  • Ulrich Abel,
  • Ana Maria Acu,
  • Margareta Heilmann,
  • Ioan Ra ̧sa

摘要

This paper furthers the study of the operators \(M_{n,j,\nu }\) , which preserve the functions 1 and \(x^j\) and reduce to the genuine Bernstein-Durrmeyer operators when \(j=\nu =1\) . The focus is on key properties of these operators, particularly examining their moments and the rate of convergence in terms of the modulus of continuity. Additionally, new results are provided regarding the behavior of \(M_{n,j,\nu }\) with respect to \(\{1, x^j\}\) -convex functions and the operators’ shape-preserving properties.