MathDB

Let

C

be a nonempty closed bounded subset of the real line and

f: C\to C

be a nondecreasing continuous function. Show that there exists a point

p\in C

such that f(p) \equal{} p. (A set is closed if its complement is a union of open intervals. A function

g

is nondecreasing if

g(x)\le g(y)

for all

x\le y

Problem Statement