Neural Networks of the Rational r-th Powers of the Multivariate Bernstein Operators

Abstract

In this study, a novel neural network for the multivariance Bernstein operators' rational powers was developed. A positive integer is required by these networks. In the space of all real-valued continuous functions, the pointwise and uniform approximation theorems are introduced and examined first. After that, the Lipschitz space is used to study two key theorems. Additionally, some numerical examples are provided to demonstrate how well these neural networks approximate two test functions. The numerical outcomes demonstrate that as input grows, the neural network provides a better approximation. Finally, the graphs used to represent these neural network approximations show the average error between the approximation and the test function.