On the approximation of the step function by some sigmoid functions

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On the approximation of the step function by some sigmoid functions

Iliev, A.; Kyurkchiev, N.; Markov, S.

Mathematics and computers in simulation, March 2017, 2017-03-00, Volume: 133

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In this note the Hausdorff approximation of the Heaviside step function by several sigmoid functions (log–logistic, transmuted log–logistic and generalized logistic functions) is considered and precise upper and lower bounds for the Hausdorff distance are obtained. Numerical examples, that illustrate our results are given, too.

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