Quantitative estimates involving K-functionals for neural network type operators

In the present paper, quantitative estimates for the neural network (NN) operators of the Kantorovich type, have been proved. Firstly, the modulus of continuity of the function being approximated has been used in order to estimate the approximation error in the uniform norm. Finally, a Peetre K-functional has been employed to obtain a quantitative upper bound in $L^p$-norm. At the end, several examples of sigmoidal activation functions for the above NN type operators have been provided.