Global Universality of the Two-Layer Neural Network with the k-Rectified Linear Unit

This paper concerns the universality of the two-layer neural network with the k-rectified linear unit activation function with k=1,2,… with a suitable norm without any restriction on the shape of the domain in the real line. This type of result is called global universality, which extends the previous result for k=1 by the present authors. This paper covers k-sigmoidal functions as an application of the fundamental result on k-rectified linear unit functions.