Convergence in Orlicz spaces by means of the multivariate max-product neural network operators of the Kantorovich type and applications

In this paper, convergence results in a multivariate setting have been proved for a family of neural network operators of the max-product type. In particular, the coefficients expressed by Kantorovich type means allow to treat the theory in the general frame of the Orlicz spaces, which includes as particular case the Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p$$\end{document}-spaces. Examples of sigmoidal activation functions are discussed, for the above operators in different cases of Orlicz spaces. Finally, concrete applications to real-world cases have been presented in both univariate and multivariate settings. In particular, the case of reconstruction and enhancement of biomedical (vascular) image has been discussed in detail.