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.