Question: Please help me with this problem, thank you. Let (X, (1) be a complete metric space and f z X > X. It is called

Please help me with this problem, thank you.

Let (X, (1) be a complete metric space and f z X > X. It is called a contraction iff Elc E [0, 1) such that for all :1:,y 6 X, d(f(a:), f(y)) 5 cd(:z:,y). Prove that in this case there exists a unique xed point a E X i.e. a unique element of X with f (a) = a. Hint: Pick a: E X and look at the sequence 2:, f (x), f o f (1:)

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