Throughout (X , ,0) will denote a metric space. R denotes the set of real numbers. For a metric space X, C(X) will denote the normed vector space consisting of the bounded continuous functions f : X a R with the supremum norm, Hf\" : supmex |f(z)l. Let h : [a, b] - R be continuous, and let K : [a, b] x [a, b] - R be continuous and suppose that M is a positive number such that | K(s, t) | K(x, y)u(y) dy. a (Here the integral is the Riemann integral.) [Hint: Define F : C([a, b]) - C([a, b]) via F(u) = v where v(x) = h(x) +> S K(x, y)u(y) dy. Show that F is a contraction (with respect to the supremum norm on C([a, b]); the latter is complete).]