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In this paper we study the theory of the so-called Kantorovich max-productneural network operators in the setting of Orlicz spaces $L^{\varphi}$. Theresults here proved, extend those given by Costarelli and Vinti in ResultMath., 2016, to a more general context. The main advantage in studying neuralnetwork type operators in Orlicz spaces relies in the possibility toapproximate not necessarily continuous functions (data) belonging to differentfunction spaces by a unique general approach. Further, in order to derivequantitative estimates in this context, we introduce a suitable K-functional in$L^{\varphi}$ and use it to provide an upper bound for the approximation errorof the above operators. Finally, examples of sigmoidal activation functionshave been considered and studied in details.

Approximation results in Orlicz spaces for sequences of Kantorovich max-product neural network operators