Some density results by deep Kantorovich type neural network operators

In this paper, we prove density results by using deep Kantorovich type neural network operators. Firstly, we define a two layer neural network operator and prove the density results in the spaces C(I) and Lp(I) for p >= 1, where I := [-1, 1]. Then we extend it to a multi-layer neural network operator and prove the corresponding density results. Our study provides a generalizations of the well known single layer Kantorovich type neural network operator in terms of its deeper version.(c) 2023 Elsevier Inc. All rights reserved.