On the $L^p$-Convergence and Denoising Performance of Durrmeyer-Type Max-Min Neural Network Operators

Berke Şahin; İsmail Aslan

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arXiv · 2601.22174

On the $L^p$-Convergence and Denoising Performance of Durrmeyer-Type Max-Min Neural Network Operators

Berke Şahin·İsmail Aslan

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Abstract

In this paper, we investigate Durrmeyer-type generalizations of maximum-minimum neural network operators. The primary objective of this study is to establish the convergence of these operators in the $L^{p}$ norm for functions $f\in L^{p}([a,b],[0,1])$ with $1\leq p<\infty$. To this end, we analyze the properties of sigmoidal functions and maximum-minimum operations, subsequently establishing the convergence of the proposed operator in pointwise, supremum, and $L^{p}$ norms. Furthermore, we derive quantitative estimates for the rates of convergence. In the applications section, numerical and graphical examples demonstrate that the proposed Durrmeyer-type operators provide smoother approximations compared to Kantorovich-type and standard max-min operators. Finally, we highlight the superior filtering performance of these operators in signal analysis, validating their effectiveness in both approximation and data processing tasks.

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Berke Şahin, İsmail Aslan. 2026-01-24. On the $L^p$-Convergence and Denoising Performance of Durrmeyer-Type Max-Min Neural Network Operators. https://arxiv.org/abs/2601.22174

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