In this paper, we approximate to functions in N-dimension by means of nonlinear integral operators of the convolution type. Our approximation is based on not only the uniform norm but also the variation semi-norm in Tonelli’s sense. We also study the rates of convergence. To get more general results we mainly use regular summability methods in the approximation. We construct some significant applications including the Cesàro approximation, the almost approximation, the rates of convergence based on certain summability methods. Furthermore, we display some graphical illustrations verifying the approximation and evaluate numerical computations giving approximation errors.

在本文中，我们通过卷积类型的非线性积分算子来逼近N维函数。我们的逼近不仅基于统一范数，而且还基于Tonelli的变分半范数。我们还研究了收敛速度。为了获得更一般的结果，我们主要在近似中使用常规的可加性方法。我们构造了一些重要的应用程序，包括Cesàro逼近，几乎逼近，基于某些可加性方法的收敛速度。此外，我们显示了一些图形插图来验证近似值并评估给出近似误差的数值计算。