Fixed Point
Fixed Point
Fixed Point
Every closure operator on a poset has many fixed points; these are the "closed elements" with respect to the closure
operator, and they are the main reason the closure operator was defined in the first place.
See also
• Atiyah–Bott fixed-point theorem
• Borel fixed-point theorem
• Brouwer fixed point theorem
• Caristi fixed point theorem
• Diagonal lemma
• Fixed point property
• Injective metric space
• Kakutani fixed-point theorem
• Kleene fixpoint theorem
• Topological degree theory
• Woods Hole fixed-point theorem
References
• Agarwal, Ravi P.; Meehan, Maria; O'Regan, Donal (2001). Fixed Point Theory and Applications. Cambridge
University Press. ISBN 0-521-80250-4.
• Aksoy, Asuman; Khamsi, Mohamed A. (1990). Nonstandard Methods in fixed point theory. Springer Verlag.
ISBN 0-387-97364-8.
• Border, Kim C. (1989). Fixed Point Theorems with Applications to Economics and Game Theory. Cambridge
University Press. ISBN 0-521-38808-2.
• Brown, R. F. (Ed.) (1988). Fixed Point Theory and Its Applications. American Mathematical Society.
ISBN 0-8218-5080-6.
• Dugundji, James; Granas, Andrzej (2003). Fixed Point Theory. Springer-Verlag. ISBN 0-387-00173-5.
• Kirk, William A.; Goebel, Kazimierz (1990). Topics in Metric Fixed Point Theory. Cambridge University Press.
ISBN 0-521-38289-0.
• Kirk, William A.; Khamsi, Mohamed A. (2001). An Introduction to Metric Spaces and Fixed Point Theory. John
Wiley, New York.. ISBN 978-0-471-41825-2.
• Kirk, William A.; Sims, Brailey (2001). Handbook of Metric Fixed Point Theory. Springer-Verlag.
ISBN 0-7923-7073-2.
• Šaškin, Jurij A; Minachin, Viktor; Mackey, George W. (1991). Fixed Points. American Mathematical Society.
ISBN 0-8218-9000-X.
Fixed point theorem 3
External links
• Fixed Point Method [2]
References
[1] The foundations of program verification, 2nd edition, Jacques Loeckx and Kurt Sieber, John Wiley & Sons, ISBN 0 471 91282 4, Chapter 4;
theorem 4.24, page 83, is what is used in denotational semantics, while Knaster–Tarski theorem is given to prove as exercise 4.3–5 on page
90.
[2] http:/ / www. math-linux. com/ spip. php?article60
Article Sources and Contributors 4
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