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.].
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Grzegorz Lewicki, G. Marino, Approximation by Superpositions of a Sigmoidal Function. Z. Anal. Anwend. 22 (2003), no. 2, pp. 463–470DOI 10.4171/ZAA/1156