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The discrete dynamics of monotonically decomposable maps. (English) Zbl 1118.65057
Summary: We extend results of J.-L. Gouzé and K. P. Hadeler [Nonlinear World 1, 23–34 (1994; Zbl 0803.65076)] concerning the dynamics generated by a map on an ordered metric space that can be decomposed into increasing and decreasing parts. Our main results provide sufficient conditions for the existence of a globally asymptotically stable fixed point for the map. Applications to discrete-time, stage-structured population models are given.
65J15Equations with nonlinear operators (numerical methods)
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47H07Monotone and positive operators on ordered topological linear spaces
92D25Population dynamics (general)
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