Stability of coincidence points and properties of covering mappings
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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.
Key wordscoincidence point set-valued mapping covering mapping metric space Lipschitzian mapping generalized Hausdorff metric complete space
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