About convex hull and fixed point

[sapporozoe]

First, I wonder whether I can put the post here...

Given
X=[0,1]^2

a(x)={y in X:||y-x||>=1/4}

b(x)is the convex hull of a(x).

Identify the set of fixed points.

My answer is 3/4>=x>=1/4, 3/4>=y>=1/4, but I am not sure...

What if we have a(x)={y in X:||y-x||>=1/2}? (My answer is x=1/2 or y=1/2)

Thanks.

 

[EnumaElish]

What is the definition of convex hull? Of fixed point?