Abstract

In this paper we compute the rates of convergence of power series statistical convergence of sequences of positive linear operators. We also investigate some Korovkin type approximation properties of the \(q\)-Meyer–König and Zeller operators and Durrmeyer variant of the \(q\)-Meyer–König and Zeller operators via power series statistical convergence. We show that the approximation results obtained in this paper expand some previous approximation results of the corresponding operators.

中文翻译：

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正线性算子的幂级数统计收敛速率和$$ \ boldsymbol {q} $$ -Meyer–Köni̇g和Zeller算符的幂级数统计收敛速率

摘要

在本文中，我们计算幂级数的收敛速率，对正线性算子序列进行统计收敛。我们也研究了一些Korovkin型逼近性能\（Q \） -Meyer -柯尼希和Zeller算子和的Durrmeyer算子的变体\（Q \）通过幂级数统计收敛-Meyer -柯尼希和Zeller算。我们表明，本文获得的逼近结果扩展了相应算子的某些先前逼近结果。