### Abstract

Non-autonomous first order difference equation of the form (Formula Presented) is considered where (Formula Presented) is a continuous function satisfying the negative feedback assumption (Formula Presented) and (Formula Presented) is a non-negative sequence. Sufficient conditions for the global asymptotic stability of the zero solution are derived in terms of the attractivity of the fixed point x_{*}=0 under the iterations of distinct maps of the family of one-dimensional maps (Formula Presented) The principal motivation for consideration of the difference equation and the corresponding family of interval maps comes from a problem of asymptotic behavior in differential equations with piece-wise constant argument (DEPCA).

Original language | English (US) |
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Title of host publication | Difference Equations and Discrete Dynamical Systems with Applications - 24th ICDEA 2018 |

Editors | Martin Bohner, Stefan Siegmund, Roman Šimon Hilscher, Petr Stehlík |

Publisher | Springer |

Pages | 231-250 |

Number of pages | 20 |

ISBN (Print) | 9783030355012 |

DOIs | |

State | Published - Jan 1 2020 |

Event | 24th International Conference on Difference Equations and Applications, ICDEA 2018 - Dresden, Germany Duration: May 21 2018 → May 25 2018 |

### Publication series

Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 312 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Conference

Conference | 24th International Conference on Difference Equations and Applications, ICDEA 2018 |
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Country | Germany |

City | Dresden |

Period | 5/21/18 → 5/25/18 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Difference Equations and Discrete Dynamical Systems with Applications - 24th ICDEA 2018*(pp. 231-250). (Springer Proceedings in Mathematics and Statistics; Vol. 312). Springer. https://doi.org/10.1007/978-3-030-35502-9_10