Best neural approximation for 2-quasi inner product spaces

Abstract

Many researchers studied two-normed spaces for objects of function approximation. Also, neural networks are great instruments for function approximation from function spaces, especially, Lebesque spaces (Lp ). In this paper, the aim is to approximate Lebesque integrable functions via two-quasi inner product that is defined here in terms of two-norm. Moreover, there is a definition of a special type of neural network with special weights to estimate the approximation error, which is equivalent to the modulus of smoothness of functions of study. Estimates of infimum and supremum bounds so that the modulus of smoothness is involved in each bound. It is interesting to investigate more work related to what we presented in this study, not only for those fields of neural network function approximation, but also to approximate functions by various types of operators.