Remarks on microperiodic multifunctions

Document Type : Research Paper

Author

AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland.

Abstract

It is well known that a microperiodic function mapping a topological group into reals, which is continuous at some point is constant. We introduce the notion of a microperiodic multifunction, defined on a topological group with values in a metric space, and study regularity conditions implying an analogous result. We deal with Vietoris and Hausdorff continuity concepts.

Stability of microperiodic multifunctions is considered, namely we show that an approximately microperiodic multifunction is close to a constant one, provided it is continuous at some point. As a consequence we obtain stability result for an approximately microperiodic single-valued function.

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References

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History

  • Receive Date: 20 February 2014
  • Revise Date: 27 October 2014
  • Accept Date: 13 February 2015

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