The approximation operators with sigmoidal functions

Zhixiang Chen, Feilong Cao

Abstract: The aim of this paper is to investigate the error which results from the method of approximation operators with logarithmic sigmoidal function. By means of the method of extending functions, a class of feed-forward neural network operators is introduced. Using these operators as approximation tools, the upper bounds of errors, in uniform norm, approximating continuous functions, are estimated. Also, a class of quasi-interpolation operators with logarithmic sigmoidal function is constructed for approximating continuous functions defined on the total real axis.