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Parametrized Hyperbolic Tangent Induced Banach Space Valued Ordinary and Fractional Neural Network Approximation. |
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PP: 597-621 |
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doi:10.18576/pfda/090406
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Author(s) |
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George A. Anastassiou,
Seda Karateke,
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Abstract |
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| Here we examine 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 establishing 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 function generated by a parametrized hyperbolic tangent function, which is a 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.
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