SoftMax Neural Best Approximation

Neural networks have a great place in approximating nonlinear functions, especially those Lebesgue integrable functions that are approximated by FNNs with one hidden layer and sigmoidal functions. Various operators of neural networks have been defined and achieved to get good rates of approximation depending on the modulus of smoothness. Here we define a new neural network operator with a generalized sigmoidal function (SoftMax) to improve the rate of approximation of a Lebesgue integrable function L_p, with p < 1, to be estimated using modulus of smoothness of order k. The importance of choosing SoftMax function as an activation function is its flexible properties and various applications.