Contraction Mapping Principle
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Show that none of the following mappings f:X→X have a fixed point and explain why the Contraction Mapping Principle is not contradicted:
X=(0,1)⊆R and f(x)=x/2 "for " x" in" X
X=R and f(x)=x+1 "for " x" in" X
X={(x,y) "in" R^2│x^2+y^2=1}"and" f(x,y)=(-y,x) "for " (x,y) "in" X
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Contraction Mapping Principle is utilized.
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Contraction Mapping Principle: Let (X,d) is a non-empty complete metric space. Let T: X --> X is a contraction mapping, where there is a nonnegative number q<1, such that d(T(x), T(y)) <= qd(x,y), then there is a ...
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