Proves first UATs for k-times differentiable nonlinear operators and their derivatives via OL architectures uniformly on compact sets in weighted Bastiani-Sobolev spaces on general Banach spaces.
Maps That Are Continuously Differentiable in the Michal and Bastiani Sense But Not in the Fréchet Sense.Journal of Mathematical Sciences, 259(6):761–774
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Universal Approximation of Nonlinear Operators and Their Derivatives
Proves first UATs for k-times differentiable nonlinear operators and their derivatives via OL architectures uniformly on compact sets in weighted Bastiani-Sobolev spaces on general Banach spaces.