标题： 幂级数统计收敛和一个抽象的Korovkin型逼近定理 显示英文标题

标题： Power series statistical convergence and an abstract Korovkin-type approximation theorem

摘要： 本文在一般空间中建立了一个抽象的Korovkin型逼近定理，将逼近论的框架扩展到更广泛的上下文中。 支持该定理的一个关键结果是证明任何$P$-统计收敛序列在密度$1$集上包含一个经典收敛子序列，这在分析中起到基础作用。 作为结论，我们研究了线性算子的$r$阶广义形式的收敛性，这些形式可能不具有正性，并提出了针对周期函数的Korovkin型逼近定理，均利用$P$-统计收敛。 这些贡献推广并改进了逼近论中的现有结果，提供了新颖的见解和方法，得到了实际例子和推论的支持。 显示英文摘要

摘要： This paper establishes an abstract Korovkin-type approximation theorem in general spaces, extending the framework of approximation theory to accommodate broader contexts. A critical result supporting this theorem is the proof that any $P$-statistically convergent sequence contains a classically convergent subsequence over a density $1$ set, which plays a foundational role in the analysis. As a conclusion, we investigate the convergence of the $r$-th order generalization of linear operators, which may lack positivity, and present a Korovkin-type approximation theorem for periodic functions, both utilizing $P$-statistical convergence. These contributions generalize and improve existing results in approximation theory, providing novel insights and methodologies, supported by practical examples and corollaries.