Monotone flows and order intervals. (English) Zbl 0803.65076

Gouzé, J.-L.; Hadeler, K. P.

Nonlinear World 1, No. 1, 23-34 (1994).

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)

MSC:

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

Keywords:

monotone flows; order intervals; fixed point iterations; linear space; partial order; dynamical system; convergence; error estimates