The approximation operators with sigmoidal functionsI

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.