The main purpose of the present article is to construct a newly Szász-Jakimovski-Leviatan-type positive linear operators in the Dunkl analogue by the aid of Appell polynomials. In order to investigate the approximation properties of these operators, first we estimate the moments and obtain the basic results. Further, we study the approximation by the use of modulus of continuity in the spaces of the Lipschitz functions, Peetres K-functional, and weighted modulus of continuity. Moreover, we study -statistical convergence of operators and approximation properties of the bivariate case.

中文翻译：

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Szász-Jakimovski-Leviatan型算子通过Appell多项式的逼近

本文的主要目的是借助Appell多项式在Dunkl类似物中构造一个新的Szász-Jakimovski-Leviatan型正线性算子。为了研究这些算子的逼近性质，首先我们估计矩并获得基本结果。此外，我们在Lipschitz函数，Peetres K函数和加权连续模量的空间中使用连续模量来研究近似值。此外，我们研究-算子的统计收敛性和双变量情况的逼近性质。