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Line 22: ==Applications== A standard application is the proof of the [[Picard-~~Lindelöf~~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. ==Converses==

Banach fixed-point theorem: Difference between revisions