In this paper, we state a Korovkin-type theorem for uniform approximation of functions, belonging to a class generated by multivariable function of modulus of continuity, by the sequence of multivariate positive linear operators. Then, using this theorem, we investigate the corresponding uniform approximation result for the multivariate Bleimann, Butzer and Hahn operators which are not in a tensor product design. Moreover, we give an elementary proof that these operators are non-increasing in n when the attached function is convex and non-increasing and we add a graphical example.

中文翻译：

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关于多元Bleimann，Butzer和Hahn运算符

在本文中，我们陈述了一个Korovkin型定理，用于函数的均匀逼近，该函数属于通过多元正线性算子序列由连续模数的多元函数生成的一类。然后，使用该定理，我们研究了不在张量积设计中的多元Bleimann，Butzer和Hahn算子的相应一致逼近结果。此外，我们给出了基本证明，即当附加函数为凸且不增加时，这些运算符的n不增加，并添加了一个图形示例。