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Monotone flows and order intervals. (English) Zbl 0803.65076
Fixed point iterations in a linear space \(X\) with a partial order \(\leq\) are considered for a mapping \(H = F - G : X \mapsto X\), in which the mappings \(F\), \(G\) are monotone increasing. By embedding the iteration into a dynamical system the authors discuss convergence and error estimates for discrete and continuous problems. They show that both the decomposition \(H=F-G\) and proper initial points are essential for the convergence of the iterations.
Reviewer: Z.Mei (Toowoomba)

65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
47J25 Iterative procedures involving nonlinear operators
47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces