Approximation by a Kantorovich–Shilkret quasi-interpolation neural network operator

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 ℝN, N ∈ 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])