Stability of coincidence points and properties of covering mappings
- 1 August 2009
- journal article
- Published by Pleiades Publishing Ltd in Mathematical Notes
- Vol. 86 (1-2), 153-158
- https://doi.org/10.1134/s0001434609070177
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 (α–ɛ)-covering for an arbitrary ɛ > 0.Keywords
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