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<p>In this paper, approximation and shape preserving properties for the so-called neural network (NN) operators have been faced. First, the case of the general NN operators based on sigmoidal function has been considered; moreover, theorems relating to uniform convergence, Korovkin-type results, and endpoint behavior have been also obtained. Furthermore, the special case of NN operators based on the ramp function and on the central B-splines, respectively, have been taken into account.</p>

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Approximation and Shape Preserving Properties of Neural Network Operators

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月15日

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  • Ana-Maria Acu,
  • Danilo Costarelli,
  • Ioan Raşa,
  • Gianluca Vinti

摘要

In this paper, approximation and shape preserving properties for the so-called neural network (NN) operators have been faced. First, the case of the general NN operators based on sigmoidal function has been considered; moreover, theorems relating to uniform convergence, Korovkin-type results, and endpoint behavior have been also obtained. Furthermore, the special case of NN operators based on the ramp function and on the central B-splines, respectively, have been taken into account.