b- Let f: [0, 1] [0, 1] be a mapping. Assume that for any z, y [0, 1], it holds that f(x)-f(y)| x-yl. Let a [0, 1] be fixed and let fn : [0, 1] R be the sequence of functions defined by z (0,1), fn(x) = f ( a + (1 - 1) ). (i) Prove that for each n E N, fn admits a fixed point , [0, 1]. (10 marks) VnEN and