Question: Q5: a) Let n be a bounded open set in R, and let o be a continuous map of n - R such that for

Q5: a) Let n be a bounded open set in R", and let o be a continuous map of n - R" such that for some fixed z E n (x) - z+ 1(x - z), xcan, 1> 1. Then @ has a fixed point in n. (5 Marks) b) If m is odd, f is a bounded, open subset of IR" containing the origin, and o is a continuous map of n - R" such that 0 @ 4(80), then there is an x E on such that (x) = Ax with 1 # 0. (5 Marks)Q5: a) Let n be a bounded open set in R", and let o be a continuous map of n - R" such that for some fixed z E n (x) - z+ 1(x - z), xcan, 1> 1. Then @ has a fixed point in n. (5 Marks) b) If m is odd, f is a bounded, open subset of IR" containing the origin, and o is a continuous map of n - R" such that 0 @ 4(80), then there is an x E on such that (x) = Ax with 1 # 0.

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