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

  • George A. AnastassiouEmail author
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 190)


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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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of MemphisMemphisUSA

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