In this paper, we present a Durrmeyer type generalization of parametric Bernstein operators. Firstly, we study the approximation behaviour of these operators including a local and global approximation results and the rate of approximation for the Lipschitz type space. The Voronovskaja type asymptotic formula and the rate of convergence of functions with derivatives of bounded variation are established. Finally, the theoretical results are demonstrated by using MAPLE software.

中文翻译：

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参数 Bernstein 算子的 Durrmeyer 型推广

在本文中，我们提出了参数 Bernstein 算子的 Durrmeyer 型泛化。首先，我们研究了这些算子的逼近行为，包括局部和全局逼近结果以及 Lipschitz 类型空间的逼近率。建立了Voronovskaja型渐近公式和具有有界变分导数的函数的收敛速度。最后，利用 MAPLE 软件对理论结果进行了验证。