Journal of Applied and Pure Mathematics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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DEGREE OF APPROXIMATION BY KANTOROVICH-CHOQUET QUASI-INTERPOLATION NEURAL NETWORK OPERATORS REVISITED

  • GEORGE A., ANASTASSIOU (Department of Mathematical Sciences, University of Memphis)
  • Received : 2022.04.11
  • Accepted : 2022.11.04
  • Published : 2022.11.30
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Abstract

In this article we exhibit univariate and multivariate quantitative approximation by Kantorovich-Choquet type quasi-interpolation neural network operators with respect to supremum norm. This is done with rates using the first univariate and multivariate moduli of continuity. We approximate continuous and bounded functions on ℝN , N ∈ ℕ. When they are also uniformly continuous we have pointwise and uniform convergences. Our activation functions are induced by the arctangent, algebraic, Gudermannian and generalized symmetrical sigmoid functions.

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References

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