Abstract
In a partially ordered space, the method xn+1 = L+xn+ − N+xn- − L−y+ + N− yn- + r, yn+1 = N+y+ − L+yn- − N−xn+ + L−x− + t of successive approximation is developed in order to enclose the solutions of a set of linear fixed point equations monotonously. The method works if only the inequalities x0 ≤ y0, x0 ≤ x1, y1 ≤ y0 related to the starting elements are satisfied. In finite-dimensional spaces suitable starting vectors can be computed if a sufficiently good approximation for the fixed points is known.
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