Ordinary and Fractional Approximation by Non-additive Integrals: Choquet, Shilkret and Sugeno Integral Approximators pp 241-251 | Cite as

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

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## 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]).

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