Journal of Applied and Pure Mathematics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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GENERALIZED SYMMETRICAL SIGMOID FUNCTION ACTIVATED NEURAL NETWORK MULTIVARIATE APPROXIMATION

  • ANASTASSIOU, GEORGE A. (Department of Mathematical Sciences, University of Memphis)
  • Received : 2022.04.04
  • Accepted : 2022.06.21
  • Published : 2022.07.30
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Abstract

Here we exhibit multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or ℝN, N ∈ ℕ, by the multivariate normalized, quasi-interpolation, Kantorovich type and quadrature type neural network operators. We treat also the case of approximation by iterated operators of the last four types. These approximations are achieved by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order Fréchet derivatives. Our multivariate operators are defined by using a multidimensional density function induced by the generalized symmetrical sigmoid function. The approximations are point-wise and uniform. The related feed-forward neural network is with one hidden layer.

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References

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