Approximation theorems for a family of multivariate neural network operators in Orlicz-type spaces

Abstract

In this paper, we study the theory of a Kantorovich version of the multivariate neural network operators. Such operators, are activated by suitable kernels generated by sigmoidal functions. In particular, the main result here proved is a modular convergence theorem in Orlicz spaces. As special cases, convergence theorem in $$L^p$$ -spaces, interpolation spaces, and exponential-type spaces can be deduced. In general, multivariate approximations by constructive neural network algorithms are useful for applications to neurocomputing processes involving high dimensional data. At the end of the paper, several examples of activation functions of sigmoidal-type for which the above theory holds have been described.