Best neural simultaneous approximation

Hawraa Abbas Almurieb (University of Babylon)
Eman S. Bhaya (University of Babylon)

Indonesian Journal of Electrical Engineering and Computer Science
Vol 20, No 3: December 2020

For many years, approximation concepts has been investigated in view of neural networks for the several applications of the two topics. Researchers studied simultaneous approximation in the 2-normed space and proved essential theorems concern with existence, uniqueness and degree of best approximation. Here, we define a new 2-norm in Lp-space, with p<1, so we call it Lp quasi 2- normed space (Lp,2). The set of approximations is a space of feedforward neural networks that is constructed in this paper. Existence and uniqueness of best neural approximation for a function from  is proved, describing the rate of best approximation in terms of modulus of smoothness.