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 b Let f 0, 1 0, 1...

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b- Let f: [0, 1] [0, 1] be a mapping. Assume that for any z,...

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b- Let ( f:[0,1] ightarrow[0,1] ) be a mapping. Assume that for any ( x, y in[0,1] ), it holds that [ |f(x)-f(y)| le

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b- Let f: [0, 1] [0, 1] be a mapping. Assume that for any z,...

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