Abstract
AbstractHere we give the univariate quantitative approximation of real and complex valued continuous functions on a compact interval or all the real line by quasi-interpolation sigmoidal neural network operators. This approximation is obtained by establishing Jackson type inequalities involving the modulus of continuity of the engaged function or its high order derivative. The operators are defined by using a density function induced by the logarithmic sigmoidal function. Our approximations are pointwise and with respect to the uniform norm. The related feed-forward neural network is with one hidden layer. This chapter relies on [4].
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