. Show that f has a unique fixed point.
Mathematics Homework Solutions
#88929
Show that the given type of function on a compact metric space has a unique fixed point.
Assume that (X, d) is a compact metric space, and let f: X -> X be a function such that the inequality d(f(x), f(y)) < d(x, y) holds for all distinct elements x, y in X. Show that f has a unique fixed point.
See attached file for full problem description.
The following is proved in detail: If the indicated type of function has fixed points "a" and "b", then a = b.
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