On the row sum criterion and the convergence of some iterative processes

Summary The well known row sum criterion (in German Zeilensummen-kriterium) is reformulated for transformations on Banach spaces with cones, and some sufficient conditions guaranteeing the convergence ofJacobi, Gauss-Seidel and successive over-relaxation iterations are derived, similar to those given byWalter 12] andKulisch 3] for linear algebraic systems.