The purpose of the present paper is to obtain the degree of approximation in terms of a Lipschitz type maximal function for the Kantorovich type modification of Jakimovski–Leviatan operators based on multiple Appell polynomials. Also, we study the rate of approximation of these operators in a weighted space of polynomial growth and for functions having a derivative of bounded variation. A Voronvskaja type theorem is obtained. Further, we illustrate the convergence of these operators for certain functions through tables and figures using the Maple algorithm and, by a numerical example, we show that our Kantorovich type operator involving multiple Appell polynomials yields a better rate of convergence than the Durrmeyer type Jakimovski Leviatan operators based on Appell polynomials introduced by Karaisa (2016).

中文翻译：

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涉及多个Appell多项式的Kantorovich类型的Jakimovski–Leviatan运算符

本文的目的是获得基于多个Appell多项式的Jakimovski–Leviatan算子的Kantorovich型修改的Lipschitz型最大函数的近似程度。同样，我们研究了在多项式增长的加权空间中以及对于具有有限变化导数的函数，这些算子的逼近率。获得Voronvskaja型定理。此外，我们使用Maple算法通过表格和图形说明了这些算子对于某些函数的收敛性，并通过一个数值示例，表明与多个Durrmeyer类型的Jakimovski Leviatan相比，涉及多个Appell多项式的Kantorovich类型算子产生了更高的收敛速度。运算符基于Karaisa（2016）引入的Appell多项式。