What question did this study set out to answer?

The aim is to explore quantitative approximation using Kantorovich–Choquet-type neural networks for various function classes.

March 21, 2026Open Access

Multiple-Composite Quantitative Approximation by Multivariate Kantorovich–Choquet Neural Networks

GAGeorge A. AnastassiouUniversity of Memphis

Key Points

The aim is to explore quantitative approximation using Kantorovich–Choquet-type neural networks for various function classes.
Studied both univariate and multivariate quantitative approximation.
Utilized multi-composite Kantorovich–Choquet-type quasi-interpolation neural networks.
Analyzed convergence rates based on univariate and multivariate moduli of continuity.
Applied estimates for continuous and bounded non-negative functions.
Examined pointwise and uniform convergence with Lp estimates.
Achieved convergence rates for approximation under the supremum norm.
Demonstrated pointwise and uniform convergence for uniformly continuous functions.
Confirmed Lp estimates for the functions approximated.

Abstract

In this work we study the univariate and multivariate quantitative approximation by multi-composite Kantorovich–Choquet-type quasi-interpolation neural network operators with respect to the supremum norm. This is achieved with rates via the first univariate and multivariate moduli of continuity. We approximate continuous and bounded non-negative functions on RN,N∈N. When they are also uniformly continuous we have pointwise and uniform convergences, plus Lp estimates. Our multi-composite activation functions are formed by general sigmoid functions.

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