Convergence for a family of neural network operators in Orlicz spaces

Abstract

In this paper, we develop the theory for a family of neural network (NN) operators of the Kantorovich type, in the general setting of Orlicz spaces. In particular, a modular convergence theorem is established. In this way, we study the above family of operators in many instances of useful spaces by a unique general approach. The above NN operators provide a constructive approximation process, in which the coefficients, the weights, and the thresholds of the networks needed in order to approximate a given function f, are known. At the end of the paper, several examples of Orlicz spaces, and of sigmoidal activation functions for which the present theory can be applied, are studied in details.

Detection of thermal bridges from thermographic images by means of image processing approximation algorithms

“…For what concerns the result in the L p -setting, this can be deduced by a general theorem proved in Orlicz spaces, see e.g., [41,9,31]. Now, we point out the main steps needed to implement the algorithm for image reconstruction and enhancement based on the sampling Kantorovich operators.…”

Convergence of sampling Kantorovich operators in modular spaces with applications

“…Other examples of band-limited kernels can be generated using the so-called sigmoidal functions (see e.g., [39]). For instance, we can define:…”

A Quantitative Estimate for the Sampling Kantorovich Series in Terms of the Modulus of Continuity in Orlicz Spaces

“…For the sake of completeness, we recall that the well-known (above mentioned) sinc-function is that defined as sin(πx)/πx, if x = 0, and 1 if x = 0, see e.g., [26,27]. For other examples of kernels, see, e.g., [13,20,15,22,16].…”