Max-Min Neural Network Operators For Approximation of Multivariate Functions
This work provides efficient and stable approximation tools for theoretical and applied settings in approximation theory, though it is incremental as it extends univariate methods to multivariate cases.
The authors tackled the problem of approximating multivariate functions by developing a new framework using max-min neural network operators, resulting in pointwise and uniform convergence theorems with quantitative estimates for approximation order.
In this paper, we develop a multivariate framework for approximation by max-min neural network operators. Building on the recent advances in approximation theory by neural network operators, particularly, the univariate max-min operators, we propose and analyze new multivariate operators activated by sigmoidal functions. We establish pointwise and uniform convergence theorems and derive quantitative estimates for the order of approximation via modulus of continuity and multivariate generalized absolute moment. Our results demonstrate that multivariate max-min structure of operators, besides their algebraic elegance, provide efficient and stable approximation tools in both theoretical and applied settings.