On the Approximation of the Cut and Step Functions by Logistic and Gompertz Functions

Authors

  • Anton Iliev Iliev Paisii Hilendarski University of Plovdiv
  • Nikolay Kyurkchiev
  • Svetoslav Markov

DOI:

https://doi.org/10.11145/j.biomath.2015.10.101

Keywords:

cut function, step function, sigmoid function, logistic function, Gompertz function, squashing function, Hausdorff approximation.

Abstract

We study the uniform approximation of the sigmoid cut function by smooth sigmoid functions such as the logistic and the Gompertz functions. The limiting case of the interval-valued В  step function is В  discussed В using В  Hausdorff metric. В Various expressions for the error estimates of the corresponding uniform and Hausdorff approximations are obtained. Numerical examples are presented using CAS MATHEMATICA.

Author Biographies

Anton Iliev Iliev, Paisii Hilendarski University of Plovdiv

Nikolay Kyurkchiev

Svetoslav Markov

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Published

2015-10-30

Issue

Section

Original Articles