The purpose of this article is to introduce a Kantorovich variant of Szász-Mirakjan operators by including the Dunkl analogue involving the Appell polynomials, namely, the Szász-Mirakjan-Jakimovski-Leviatan-type positive linear operators. We study the global approximation in terms of uniform modulus of smoothness and calculate the local direct theorems of the rate of convergence with the help of Lipschitz-type maximal functions in weighted space. Furthermore, the Voronovskaja-type approximation theorems of this new operator are also presented.

中文翻译：

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涉及Appell多项式的Szász-Mirakjan-Kantorovich算子的参数扩展近似

本文的目的是通过引入涉及Appell多项式的Dunkl类似物，即Szász-Mirakjan-Jakimovski-Leviatan型正线性算子，来介绍Szász-Mirakjan算子的Kantorovich变体。我们研究均匀性平滑模量方面的全局逼近，并借助加权空间中的Lipschitz型极大函数来计算收敛速度的局部直接定理。此外，还介绍了该新算子的Voronovskaja型逼近定理。