The purpose of the present paper is to introduce and study a sequence of positive linear operators defined on suitable spaces of measurable functions on $[0,\infty )$ and continuous function spaces with polynomial weights. These operators are Kantorovich type generalization of Jakimovski–Leviatan operators based on multiple Appell polynomials. Using these operators, we approximate suitable measurable functions by knowing their mean values on a sequence of subintervals of $[0,\infty )$ that do not constitute a subdivision of it. We also discuss the rate of convergence of these operators using moduli of smoothness.

中文翻译：

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使用多个Appell多项式对Szász-Mirakjan-Kantorovich算子的推广

本文的目的是介绍和研究一系列正线性算子，这些正线性算子定义在$ [0，\ infty）$的可测函数的合适空间和具有多项式权重的连续函数空间上。这些运算符是基于多个Appell多项式的Jakimovski–Leviatan运算符的Kantorovich类型概括。使用这些运算符，我们通过了解在不构成其细分的$ [0，\ infty）$子区间序列上的平均值，来近似合适的可测量函数。我们还将讨论使用平滑度模的这些算子的收敛速度。