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Mathematical Notes

, Volume 86, Issue 1–2, pp 153–158 | Cite as

Stability of coincidence points and properties of covering mappings

  • A. V. Arutyunov
Article

Abstract

Properties of closed set-valued covering mappings acting from one metric space into another are studied. Under quite general assumptions, it is proved that, if a given α-covering mapping and a mapping satisfying the Lipschitz condition with constant β < α have a coincidence point, then this point is stable under small perturbations (with respect to the Hausdorff metric) of these mappings. This assertion is meaningful for single-valued mappings as well. The structure of the set of coincidence points of an α-covering and a Lipschitzian mapping is studied. Conditions are obtained under which the limit of a sequence of α-covering set-valued mappings is an (αɛ)-covering for an arbitrary ɛ > 0.

Key words

coincidence point set-valued mapping covering mapping metric space Lipschitzian mapping generalized Hausdorff metric complete space 

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Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  • A. V. Arutyunov
    • 1
  1. 1.Peoples’ Friendship University of RussiaMoscowRussia

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