Solution
= Solution
\b[No.] The <continuous function> $f(x)=(x+1)/2$ maps $(0,1)$ into $(0,1)$, but $f(x)-x=(1-x)/2>0$ throughout the domain. Its only possible <fixed point> is the excluded endpoint one.
= Solution
\b[No.] The <continuous function> $f(x)=(x+1)/2$ maps $(0,1)$ into $(0,1)$, but $f(x)-x=(1-x)/2>0$ throughout the domain. Its only possible <fixed point> is the excluded endpoint one.