Multi-composite general neural network approximation over finite dimensional Banach spaces

George A. Anastassiou

doi:10.65112/tcmis.10051

Authors

George A. Anastassiou Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A. https://orcid.org/0000-0002-3781-9824

DOI:

https://doi.org/10.65112/tcmis.10051

Keywords:

inite dimensional Banach spaces, multi-composite general neural network operators approximation, modulus of continuity, multi-composite general accelerated approximation

Abstract

The functions under approximation here have as a domain a finite dimensional Banach space with dimension N∈N and are with values in R^N. Exploiting some topological properties of the above we are able to perform multi-composite general Neural Network multivariate approximation to the above functions. The treatment is quantitative. We produce multivariate multi-composite general Jackson type inequalities involving the modulus of continuity of the function under approximation. The established convergences are pointwise and uniform. Our technique is expected to lead to accelerated speeds of convergence.

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References

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