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Zeitschrift für Analysis und ihre Anwendungen

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Volume 22, Issue 2, 2003, pp. 463–470
DOI: 10.4171/ZAA/1156

Published online: 2003-06-30

Approximation by Superpositions of a Sigmoidal Function

Grzegorz Lewicki[1] and G. Marino[2]

(1) Jagiellonian University, Krakow, Poland
(2) Università della Calabria, Arcavacata Di Rende, Italy

We generalize a result of B. Gao and Y. Xu [J. Math. Anal. Appl. 178 (1993) 221--226] concerning the approximation of functions of bounded variation by linear combinations of a fixed sigmoidal function to the class of functions of bounded f-variation. Also, in the case of one variable, a proposition of A. R. Barron [IEEE Trans. Inf. Theory 36 (1993) 930--945] is improved. Our proofs are similar to that of Gao and Xu [loc. cit.].

Keywords: Hölder continuity property, sigmoidal function, φ-variation, uniform approximation

Lewicki Grzegorz, Marino G.: Approximation by Superpositions of a Sigmoidal Function. Z. Anal. Anwend. 22 (2003), 463-470. doi: 10.4171/ZAA/1156