Approximation by superpositions of a sigmoidal function (Q5917524)

The present paper deals with the generalization of a result due to \textit{B. Gao} and \textit{Y. Xu} [J. Math. Anal. Appl. 178, 221--226 (1993; Zbl 0783.41016)], concerning the approximation of functions of bounded variation by the linear combinations of a fixed sigmoidal function to the class of functions of bounded phi-variation. Actually the approximation of functions by superpositions of a sigmoidal function has many applications in neural network. In this paper the authors obtained only one dimensional result.