Inthispaper,weintroduceatypeofapproximationoperatorsofneuralnetworkswithsigmodalfunctionsoncompactintervals,andobtainthepointwiseanduniformestimatesoftheapproximation.Toimprovetheapproximationrate,wefurtherintroduceatypeofcombinationsofneuralnetworks.Moreover,weshowthatthederivativesoffunctionscanalsobesimultaneouslyapproximatedbythederivativesofthecombinations.Wealsoapplyourmethodtoconstructapproximationoperatorsofneuralnetworkswithsigmodalfunctionsoninfiniteintervals.
