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 -space, with so we call it quasi 2- normed space ( ). 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.