Banach fixed-point theorem: Difference between revisions

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A standard application is the proof of the [[Picard-Lindelöf theorem]] about the existence and uniqueness of solutions to certain [[ordinary differential equation]]s. The sought solution of the differential equation is expressed as a fixed point of a suitable integral operator which transforms continuous functions into continuous functions. The Banach fixed point theorem is then used to show that this integral operator has a unique fixed point.

==References==

* Vasile I. Istratescu, ''Fixed Point Theory, An Introduction'', D.Reidel, Holland (1981). ISBN 90-277-1224-7 See chapter 7.

* Andrzej Granas and James Dugundji, ''Fixed Point Theory'' (2003) Springer-Verlag, New York, ISBN 0-387-00173-5

* William A. Kirk and Brailey Sims, ''Handbook of Metric Fixed Point Theory'' (2001), Kluwer Academic, London ISBN 0-7923-7073-2

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