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Algebraic function based Banach space valued ordinary and fractional neural network approximations

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FDE2 - Fractional differential equations

Here we research the univariate quantitative approximation, ordinary and fractional, of Banach space valued continuous functions on a compact interval or all the real line by quasi-interpolation Banach space valued neural network operators. These approximations are derived by estab- lishing Jackson type inequalities involving the modulus of continuity of the engaged function or its Banach space valued high order derivative of fractional derivatives. Our operators are defined by using a density func- tion generated by an algebraic sigmoid function. The approximations are pointwise and of the uniform norm. The related Banach space valued feed-forward neural networks are with one hidden layer.

This talk is part of the Isaac Newton Institute Seminar Series series.

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