A PROOF OF TWO CONJECTURES RELATED TO THE ERDÖS-DEBRUNNER INEQUALITY

Erdos-Debrunner inequality, Areas, Extrema, p-th power mean. Abstract: In this paper we prove some results which imply two conjectures proposed by Janous on an extension to the p-th power-mean of the Erdos-Debrunner inequality relating the areas of the four sub-triangles formed by connecting three arbitrary points on the sides of a given triangle.