Radial basis function network using Lambert–Kaniadakis Wκ function

In this work the authors present a new class of radial basis functions (RBF) using functions from the $\kappa$-generalized Kaniadakis thermostatistics and the Lambert–Kaniadakis $W_{\kappa }$ function, a recent generalization of the Lambert $W$ function using the $\kappa$-exponential. Such functions are used to build neural networks of radial basis functions (RBFN). Two applications of these new RBFNs are described: In the first, we use such networks with $\kappa =1/3$ to train data that describe a time serie with additive noise. Second, we use the same RBFNs to numerically calculate the solution of Fredholm linear integral equations of the second kind.