Stability of coincidence points and properties of covering mappings |
| |
Authors: | A. V. Arutyunov |
| |
Affiliation: | 1. Peoples’ Friendship University of Russia, Moscow, Russia
|
| |
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–?)-covering for an arbitrary ? > 0. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|