On the $L^p$-Convergence and Denoising Performance of Durrmeyer-Type Max-Min Neural Network Operators
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866912861159161856 |
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| author | Şahin, Berke Aslan, İsmail |
| author_facet | Şahin, Berke Aslan, İsmail |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_22174 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the $L^p$-Convergence and Denoising Performance of Durrmeyer-Type Max-Min Neural Network Operators Şahin, Berke Aslan, İsmail Numerical Analysis 41A30, 41A25 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. |
| title | On the $L^p$-Convergence and Denoising Performance of Durrmeyer-Type Max-Min Neural Network Operators |
| topic | Numerical Analysis 41A30, 41A25 |
| url | https://arxiv.org/abs/2601.22174 |