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Brouwer
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29:24
YouTube
Bill Kinney
Fixed Point Theorems (including Contraction Mappings) and Proof Sketches
Suppose the continuous function g maps the closed interval [a,b] into itself (so g:[a,b]–»[a,b]). Then g has at least one fixed point. If g is a contraction mapping such that |g'(x)| is bounded by a positive number less than 1 on the open interval (a,b), then g has a unique fixed point. The ideas of the proofs of these are based on the ...
2.9K views
Feb 17, 2023
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