Ran, André C. M.; Reurings, Martine C. B. A fixed point theorem in partially ordered sets and some applications to matrix equations. (English) Zbl 1060.47056 Proc. Am. Math. Soc. 132, No. 5, 1435-1443 (2004). The authors prove an analogue of Banach’s fixed point theorem in partially ordered sets, and discuss several applications to linear and nonlinear matrix equations. Reviewer: Ulrich Kosel (Freiberg) Cited in 34 ReviewsCited in 830 Documents MSC: 47H10 Fixed-point theorems 15A24 Matrix equations and identities 54H25 Fixed-point and coincidence theorems (topological aspects) Keywords:fixed points; matrix equations; partially ordered sets PDFBibTeX XMLCite \textit{A. C. M. Ran} and \textit{M. C. B. Reurings}, Proc. Am. Math. Soc. 132, No. 5, 1435--1443 (2004; Zbl 1060.47056) Full Text: DOI