Banach Space Valued Neural Network by George A. Anastassiou

Author:George A. Anastassiou
Language: eng
Format: epub
ISBN: 9783031164002
Publisher: Springer International Publishing

Notation 7.22

Here , Denote by

(7.94)

(7.95)

(7.96)

and

(7.97)

We give the condensed

Theorem 7.23

Let , , n, with , is odd. Then

(i)

(7.98)

where is for

and

(ii)

(7.99)

For f uniformly continuous and in we obtain

pointwise and uniformly.

Proof

By Theorems 7.8, 7.16, 7.17 and 7.18.

Next we talk about iterated neural network approximation (see also [9]).

We give

Theorem 7.24

All here as in Theorem 7.23 and , as in (7.98). Then

(7.100)

So that the speed of convergence to the unit operator of is not worse than of

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