We investigate the approximation properties of nonlinear integral operators of the convolution type. In this approximation, we use functions of bounded variation based on the appropriate functionals. To get more general results, we consider Bell-type summability methods in the approximation. Moreover, we examine the rate of approximation. Then, using summability methods, we obtain a characterization for absolute continuity. Our examples at the end of the paper clearly demonstrate why we used summability methods rather than convergence in the conventional sense.

中文翻译：

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使用求和法的非线性积分算子的变分和近似率的收敛性

我们研究卷积型非线性积分算子的逼近性质。在这种近似中，我们基于适当的函数使用有限变化函数。为了获得更一般的结果，我们在近似中考虑了贝尔型可加性方法。此外，我们研究了近似率。然后，使用可加性方法，我们获得了绝对连续性的表征。本文末尾的示例清楚地说明了为什么我们使用可加性方法而不是常规意义上的收敛。