### Mapping, Contraction and Fixed-Point Theorem

(See attached file for full problem description with proper equations) --- 3. Let T(x) = x^2 Show that T is a contraction on (0, 1/3] , but that T has no fixed point on this interval. Does this conflict Theorem 6.4? Explain. Note: We are using the book Methods of Real Analysis by Richard R. Goldberg. This