Locally covering maps in metric spaces and coincidence points. (English) Zbl 1182.54050
The authors extend the results of the first author considering covering maps with respect to certain subsets in metric spaces. Section I is an introduction and preliminaries. Section II contains coincidence theorems for single-valued maps. In Section III a coincidence theorem for multi-valued maps is proved. In Section IV conditions are formulated which imply a local covering to be a global one. Interesting applications are contained in Section V. The authors prove the existence of a positive solution for a feedback control system governed by a semilinear differential inclusion in a separable Banach space with a cone.
Reviewer: Vassil Angelov (Sofia)
MSC:
54H25 | Fixed-point and coincidence theorems (topological aspects) |
47H04 | Set-valued operators |
47H10 | Fixed-point theorems |
47J05 | Equations involving nonlinear operators (general) |
54E40 | Special maps on metric spaces |