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

  • George A. Anastassiou Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A.
Keywords: error function based activation function, multivariate quasi-interpolation neural network approximation, Kantorovich-Shilkret type operator

Abstract

In this article 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.

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Published
2019-03-15
How to Cite
Anastassiou, G. A. (2019). Quantitative Approximation by a Kantorovich-Shilkret quasi-interpolation neural network operator. CUBO, A Mathematical Journal, 20(3), 01–11. https://doi.org/10.4067/S0719-06462018000300001