In this paper, we propose to investigate a new weighted statistical convergence by applying the Nörlund–Cesáro summability method. Based upon this definition, we prove some properties of statistically convergent sequences and a kind of the Korovkin type theorems. We also study the rate of the convergence for this kind of weighted statistical convergence and a Voronovskaya type theorem.

中文翻译：

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一些加权统计收敛以及相关的Korovkin和Voronovskaya型定理

在本文中，我们建议使用Nörlund–Cesáro可和性方法研究新的加权统计收敛。基于此定义，我们证明了统计收敛序列的某些性质和一种Korovkin型定理。我们还研究了这种加权统计收敛和Voronovskaya型定理的收敛速度。