Convergence for a family of neural network operators in Orlicz spaces. Issue 2 (27th July 2016)

• Record Type: Journal Article
• Authors: Costarelli, Danilo; Vinti, Gianluca
• Is Part Of: Mathematische Nachrichten. Volume 290:Issue 2/3(2017)
• Page Start: 226
• Page End: 235
• Publication Date: 2016-07-27
• Subjects: Sigmoidal function -- neural network operator -- Orlicz space -- modular convergence -- 41A05 -- 41A25 -- 41A30 -- 47A58; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201600006
• Languages: English
• ISSNs: 0025-584X

Abstract

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.