Best neural simultaneous approximation

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 𝐿𝑝,2 is proved, describing the rate of best approximation in terms of modulus of smoothness.