Arutyunov, Aram; Avakov, Evgeniy; Gel’man, Boris; Dmitruk, Andrei; Obukhovskii, Valeri Locally covering maps in metric spaces and coincidence points. (English) Zbl 1182.54050 J. Fixed Point Theory Appl. 5, No. 1, 105-127 (2009). 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) Cited in 1 ReviewCited in 49 Documents 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 Keywords:\(\alpha \)-covering map; locally covering map; coincidence point; fixed point; contraction map; multivalued map; control system PDFBibTeX XMLCite \textit{A. Arutyunov} et al., J. Fixed Point Theory Appl. 5, No. 1, 105--127 (2009; Zbl 1182.54050) Full Text: DOI