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Values of limit periodic sequences and functions

  • Michal Veselý EMAIL logo and Petr Hasil
Published/Copyright: May 2, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 1

Abstract

We consider limit periodic sequences and functions with values in pseudometric spaces. We construct limit periodic sequences and functions with given values. For any totally bounded countable set, we find a limit periodic sequence which attains each value from this set periodically. A corresponding result concerning such a construction of limit periodic functions is proved as well. For any totally bounded countable set which is dense in itself, we construct a limit periodic bijective map from the integers into this set. As corollaries, we obtain new results about non-almost periodic solutions of almost periodic transformable difference systems.

Keywords: limit periodic sequences; limit periodic functions; almost periodicity; asymptotic almost periodicity
MSC: Primary 11K31; 11K70; Secondary 39A06; 39A24; 42A75; 43A60; 46S40

The first author is supported by the project “Employment of Best Young Scientists for International Cooperation Empowerment” (CZ.1.07/2.3.00/30.0037) co-financed from European Social Fund and the state budget of the Czech Republic.

The second author is supported by the Czech Science Foundation under Grant P201/10/1032.

  1. This paper has been communicated by Gregor Dolinar

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Received: 2012-10-8
Accepted: 2013-4-19
Published Online: 2016-5-2
Published in Print: 2016-2-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0114
Keywords for this article
limit periodic sequences; limit periodic functions; almost periodicity; asymptotic almost periodicity

Articles in the same Issue

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  2. Prof. RNDr. Ján Jakubík, DrSc. passed away
  3. Research Article
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  5. Research Article
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  7. Research Article
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  9. Research Article
  10. Values of limit periodic sequences and functions
  11. Research Article
  12. On representation of quasi-Hopf group coalgebras
  13. Research Article
  14. On the q-Bernstein polynomials of the logarithmic function in the case q > 1
  15. Research Article
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  17. Research Article
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  19. Research Article
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  23. Research Article
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  27. Research Article
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