1. Let T be a continuous mapping from S - S where S is a closed set. Suppose that T satisfies a contraction property, i.e., 3 ye (0, 1) such that III (20) - T(y)ll = 7/x- yll, II . II can be any norm. Show that (a) There exists a unique a* s.t. T(a*) = x* (10 points) (b) The fixed point iteration starting with xo (10 points) *k+ 1 = T(Ik ) , converges to a*, i.e., limk-took = a* . Hint: In both questions a and b, first show that TK is a Cauchy sequence. And then use results in Problem 2 and the fact that T is continuous. 2. Next let T be the right-hand side of the Bellman equation, i.e. for all i (IVA) (2) = Er(i, "(i))] + > > Pijn(i)) V.(j). jEs (a) Given any V, V' such that V(i)