In this paper, we improve the order of approximation of certain operators linking Bernstein and genuine Bernstein–Durrmeyer operators. Firstly, we obtain some direct results in terms of modulus of continuity and Voronovskaja type asymptotic formula for these operators. Finally, we give some numerical examples regarding the obtained theoretical results for new constructed operators.

中文翻译：

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某些链接运算符的近似值

在本文中，我们改进了连接 Bernstein 和真正的 Bernstein-Durrmeyer 算子的某些算子的近似阶数。首先，我们在这些算子的连续性模量和 Voronovskaja 型渐近公式方面获得了一些直接结果。最后，我们给出了一些关于新构造算子获得的理论结果的数值例子。