# L p -Convergence of Kantorovich-Type Max-Min Neural Network Operators

“L p -Convergence of Kantorovich-Type Max-Min Neural Network Operators” (2026), by İsmail Aslan et al. Mathematics research paper. Original abstract below, unchanged. A free PDF is available.

- Authors: İsmail Aslan, Stefano De Marchı, Wolfgang Erb
- Published: November 4, 2026
- Field: Mathematics
- DOI: https://doi.org/10.1080/01630563.2026.2753788
- Free PDF: https://arxiv.org/pdf/2407.03329

## Abstract

In this work, we study the Kantorovich variant of max-min neural network operators, in which the operator kernel is defined in terms of sigmoidal functions. Our main aim is to demonstrate the Lp-convergence of these nonlinear operators for 1≤p<∞, which makes it possible to obtain approximation results for functions that are not necessarily continuous. In addition, we will derive quantitative estimates for the rate of approximation in the Lp-norm. We will provide some explicit examples, studying the approximation of discontinuous functions with the max-min operator, and varying additionally the underlying sigmoidal function of the kernel. Furthermore, we numerically compare the Lp-approximation error and computational time complexity of our operator with the Kantorovich variants of other prominent neural network operators. As an application, we illustrate that the Kantorovich max-min operator can offer advantages over the classical variant and the Kantorovich max-product operators when filtering noisy functions, such as biomedical ECG signals.

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