Journal of Mathematical Chemistry

, Volume 54, Issue 1, pp 109–119 | Cite as

On the Hausdorff distance between the Heaviside step function and Verhulst logistic function

  • Nikolay Kyurkchiev
  • Svetoslav Markov
Original Paper


In this note we prove more precise estimates for the approximation of the step function by sigmoidal logistic functions. Numerical examples, illustrating our results are given, too.


Sigmoid functions Logistic functions Interval functions Heaviside step function Sigmoid perceptron with one input Hausdorff distance Upper and lower bounds 



The authors greatly appreciate the referee’s suggestions.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.SofiaBulgaria

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