In this article, we establish the approximation by Durrmeyer type Jakimovski–Leviatan operators involving the Brenke type polynomials. The positive linear operators are constructed for the Brenke polynomials, and thus approximation properties for these polynomials are obtained. The order of convergence and the weighted approximation are also considered. Finally, the Voronovskaya type theorem is demonstrated for some particular case of these polynomials.

中文翻译：

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使用 Jakimovski-Leviatan 算子的 Brenke 多项式的某些近似性质

在本文中，我们通过涉及 Brenke 型多项式的 Durrmeyer 型 Jakimovski-Leviatan 算子建立近似。为 Brenke 多项式构造正线性算子，从而获得这些多项式的近似性质。收敛的阶数和加权近似也被考虑。最后，针对这些多项式的某些特殊情况，证明了 Voronovskaya 类型定理。