Abstract
In this chapter we present univariate and multivariate basic approximation by Kantorovich–Choquet type quasi-interpolation neural network operators with respect to supremum norm. This is done with rates using the first univariate and multivariate moduli of continuity. We approximate continuous and bounded functions on \(\mathbb {R}^{N},\) \(N\in \mathbb {N}\). When they are also uniformly continuous we have pointwise and uniform convergences. It follows [11].
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Anastassiou, G.A. (2019). Approximation with Rates by Kantorovich–Choquet Quasi-interpolation Neural Network Operators. In: Ordinary and Fractional Approximation by Non-additive Integrals: Choquet, Shilkret and Sugeno Integral Approximators. Studies in Systems, Decision and Control, vol 190. Springer, Cham. https://doi.org/10.1007/978-3-030-04287-5_1
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DOI: https://doi.org/10.1007/978-3-030-04287-5_1
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