2002 | OriginalPaper | Chapter
Monotone Iterative Methods
Author : Radu Precup
Published in: Methods in Nonlinear Integral Equations
Publisher: Springer Netherlands
Included in: Professional Book Archive
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The basic notion in this chapter is that of an ordered Banach space. We try to localize solutions of an operator equation u = T (u) in an ordered interval [u0, v0] of an ordered Banach space X. In addition we look for solutions which are limits of increasing or decreasing sequences of elements of X. The basic property of the operator T is monotonicity. This combined with certain properties of the ordered Banach space X guarantees the convergence of monotone sequences. Thus we may say that this chapter explores the contribution of monotonicity to compactness.