Infinitely many concrete multiple-composite quantitative approximations by different
Kantorovich—Shilkret neural network operators

Abstract. Here we research the multivariate quantitative approximation by infinitely many concrete and different multiple-composite Kantorovich—Shilkret type quasi-interpolation neural network operators with respect to supremum and \(L_{p}\) norms. This is achieved with rates via the first multivariate modulus of continuity. We approximate continuous and bounded non-negative functions on \(\mathbb{R}^{N}\), \(N\in \mathbb{N}\). When they are also uniformly continuous we have pointwise, uniform and \(L_{p}\) convergences. Complex approximation is also discussed. Our multiple-composite activation functions are formed by 7 specific known sigmoid functions.

Key words and phrases. Multi-composite specific sigmoid activation functions, quasi-interpolation neural network approximation, multi-composite Kantorovich—Shilkret type operators.