Monotone Iterative Methods

Radu Precup
Additional contact information
Radu Precup: Babeş-Bolyai University, Department of Applied Mathematics

Chapter Chapter 11 in Methods in Nonlinear Integral Equations, 2002, pp 163-194 from Springer

Abstract: 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.

Keywords: Unique Solution; Periodic Solution; Normal Cone; Positive Cone; Lower Solution (search for similar items in EconPapers)
Date: 2002
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-015-9986-3_12

Ordering information: This item can be ordered from
http://www.springer.com/9789401599863

DOI: 10.1007/978-94-015-9986-3_12

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().