Assignment:
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
Provide complete and step by step solution for the question and show calculations and use formulas.