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Multivariate Quantitative Approximation by Perturbed Kantorovich–Shilkret Neural Network Operators

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

Abstract

This chapter deals with the determination of the rate of convergence to the unit of Perturbed Kantorovich–Shilkret multivariate normalized neural network operators of one hidden layer. These are given through the multivariate modulus of continuity of the engaged multivariate function or its high order partial derivatives and that appears in the associated multivariate Jackson type inequalities. The activation function is very general and it can derive from any multivariate sigmoid or bell-shaped functions. The right hand sides of our Jackson type inequalities do not depend on the activation function. The sample functionals are Kantorovich–Shilkret type. We provide an application for the first partial derivatives of the involved function. It follows [4].

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of MemphisMemphisUSA

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