Universal Approximation Property of Weighted Approximate Identity Neural Networks

Abstract

Universal approximation property of feedforward artificial neural networks is one of the important research topics in the approximation theory of artificial neural networks. In this paper, we examine the universal approximation property of one-hidden-layer feedforward weighted approximate identity neural networks in the weighed spaces of continuous functions. To do this end, we firstly introduce the notion of weighted approximate identity. Secondly, we present two theorems by using this notion in order to show universal approximation property of weighted approximate identity neural networks in the weighed spaces of continuous functions. The obtained results develop the existence theoretical results. CENet2015 12-13 September