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<p>In this paper, we investigate approximation properties of Kantorovich type neural network operators in Orlicz spaces. We introduce the truncated discrete absolute moments and the integral absolute moments of the activation function, and use these two moments to characterize the conditions of the activation function. We obtain both the direct and the converse theorems for the approximation of the corresponding neural network operators when the moments of the activation function satisfies certain conditions.</p>

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Direct and Converse Results of Approximation by Kantorovich Type Neural Network Operators in Orlicz Spaces

  • 期刊论文

  • 发表日期：

    2025年7月23日

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  • Renyi Xue,
  • Dansheng Yu

摘要

In this paper, we investigate approximation properties of Kantorovich type neural network operators in Orlicz spaces. We introduce the truncated discrete absolute moments and the integral absolute moments of the activation function, and use these two moments to characterize the conditions of the activation function. We obtain both the direct and the converse theorems for the approximation of the corresponding neural network operators when the moments of the activation function satisfies certain conditions.