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Convergence for a family of neural network operators in Orlicz spaces
Author(s) -
Costarelli Danilo,
Vinti Gianluca
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600006
Subject(s) - mathematics , constructive , convergence (economics) , pure mathematics , modes of convergence (annotated index) , function space , operator (biology) , order (exchange) , algebra over a field , process (computing) , topological space , computer science , topological vector space , biochemistry , chemistry , isolated point , economics , economic growth , operating system , finance , repressor , transcription factor , gene
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.