Best neural simultaneous approximation

Abstract

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.