Approximation by a Kantorovich–Shilkret Quasi-interpolation Neural Network Operator

Abstract

In this chapter we present multivariate basic approximation by a Kantorovich–Shilkret type quasi-interpolation neural network operator with respect to supremum norm. This is done with rates using the multivariate modulus of continuity. We approximate continuous and bounded functions on $\mathbb {R}^{N}$, $N\in \mathbb {N}$. When they are additionally uniformly continuous we derive pointwise and uniform convergences. It follows (Anastassiou, Quantitative approximation by a Kantorovich–Shilkret quasi-interpolation neural network operator (2018) [3]).