Demonstrates shape preserving properties and approximation capabilities of neural network operators, suggesting their mathematical reliability.
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.
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Acu et al. (2026) studied this question.
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