Numerical Functional Analysis and Optimization· 2026Q1
L p -Convergence of Kantorovich-Type Max-Min Neural Network Operators
- 5citations
- Q1SCImago
- 2026year
Short summary
A new Kantorovich-type max-min neural network operator demonstrates Lp-convergence (1≤p<∞) for approximating non-continuous functions, with quantitative estimates for approximation rates.
AI-generated from the title and abstract; the full text is not read.
Key points
- Introduced a Kantorovich variant of max-min neural network operators with sigmoidal kernels.
- Demonstrated Lp-convergence (1≤p<∞) for approximating non-continuous functions.
- Derived quantitative estimates for the rate of approximation in the Lp-norm.
- Numerically compared the operator with others, showing advantages for noisy signal filtering (e.g., biomedical ECG).
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Numerical Functional Analysis and Optimization, 2026 · DOI ↗
Continue with a free account
Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.
Continue free on the webSign in with Google or Apple; no card needed. You come back to this paper.
On your phone:
Field: Applied Mathematics
Applied MathematicsMathematics