In this paper, we introduce an interesting kind of convergence for a double sequence called the uniform convergence at a point. We give an example and demonstrate a Korovkin-type approximation theorem for a double sequence of functions using the uniform convergence at a point. Then we show that our result is stronger than the Korovkin theorem given by Volkov and present several graphs. Finally, in the last section, we compute the rate of convergence.

中文翻译：

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一个点上的双重函数序列和Korovkin型逼近定理的一致收敛

在本文中，我们为双序列引入了一种有趣的收敛形式，称为点的均匀收敛。我们给出一个例子，并说明在一个点使用均匀收敛的双重函数序列的Korovkin型逼近定理。然后，我们证明了我们的结果比沃尔科夫给出的Korovkin定理更强，并给出了几个图表。最后，在最后一节中，我们计算收敛速度。