Csaba Vincze (2013)

University of Debrecen

**Excercise 5.2.1 **
*Prove that the kernel of D is convex. *

**Excercise 5.2.2 **
*Find the kernels of the following shapes in the plane. *

**Excercise 5.2.3 **
*Prove that the points *

${p}_{0},{z}_{0}\text{}and\text{}u$ |

in the proof of Krasnosselsky's theorem is not collinear.

Hint. In case of collinear points we have that p(0)=v(0) and z=z(0). Therefore H(0) separates the convex hull of B(p(0)) and u which is obviously a contradiction.