We prove asymptotic evaluations for univariate and multivariate positive linear operators. Our proofs are different from what has been used so far. As applications of our results, we find the full asymptotic evaluation for the iterates of the univariate Cesàro and Volterra operators. Moreover, we find asymptotic evaluations for the iterates of multivariate Cesàro and Volterra type operators on the k-dimensional unit cube, k-dimensional unit triangle, etc.

中文翻译：

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一些正线性算子序列的渐近求值

我们证明了单变量和多变量正线性算子的渐近评估。我们的证明与目前使用的不同。作为我们结果的应用，我们找到了单变量 Cesàro 和 Volterra 算子迭代的完整渐近评估。此外，我们找到了 k 维单位立方体、k 维单位三角形等上的多元 Cesàro 和 Volterra 类型算子的迭代的渐近评估。