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A fixed point theorem in partially ordered sets and some applications to matrix equations. (English) Zbl 1060.47056
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.

MSC:
47H10Fixed point theorems for nonlinear operators on topological linear spaces
15A24Matrix equations and identities
54H25Fixed-point and coincidence theorems in topological spaces