We consider convolution-type nonlinear integral operators endowed with Musielak-Orlicz $\varphi$-variation. Our aim is to get more powerful approximation results with the help of summability methods. In this study, we use $\varphi$-absolutely continuous functions for our convergence results. Moreover, we study the order of approximation using suitable Lipschitz class of continuous functions. A general characterization theorem for $\varphi $-absolutely continuous functions is also obtained. We also give some examples of kernels in order to verify our approximations. At the end, we indicate our approximations in figures together with some numerical computations.
Convolution type operators, $N$-dimensional nonlinear integral operators, bounded $\varphi$-variation, summability process, order of approximation
"Multivariate approximation in $\varphi$-variation for nonlinear integral operators via summability methods,"
Turkish Journal of Mathematics: Vol. 46:
1, Article 19.
Available at: https://journals.tubitak.gov.tr/math/vol46/iss1/19