Approximation by multivariate max-product Kantorovich-type operators and learning rates of least-squares regularized regression

Abstract

In a recent paper, for univariate max-product sampling operators based on general kernels with bounded generalized absolute moments, we have obtained several \begin{document}$ L^{p}_{\mu} $\end{document} convergence properties on bounded intervals or on the whole real axis. In this paper, firstly we obtain quantitative estimates with respect to a \begin{document}$ K $\end{document} -functional, for the multivariate Kantorovich variant of these max-product sampling operators with the integrals written in terms of Borel probability measures. Applications of these approximation results to learning theory are obtained.