Voronovskaja Type Theorems and High-Order Convergence Neural Network Operators with Sigmoidal Functions

In the present paper, asymptotic expansion and Voronovskaja type theorem for the neural network operators have been proved. The above results are based on the computation of the algebraic truncated moments of the density functions generated by suitable sigmoidal functions, such as the logistic functions, sigmoidal functions generated by splines and other. Further, operators with high-order convergence are also studied by considering finite linear combination of the above neural network type operators and Voronovskaja type theorems are again proved. At the end of the paper, numerical results are provided.