Abstract
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 [u 0, v 0] 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.
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© 2002 Springer Science+Business Media Dordrecht
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Precup, R. (2002). Monotone Iterative Methods. In: Methods in Nonlinear Integral Equations. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9986-3_12
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DOI: https://doi.org/10.1007/978-94-015-9986-3_12
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6114-0
Online ISBN: 978-94-015-9986-3
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