On an empty triangle with the maximum area in planar point sets

We deal with only finite point sets P in the plane in general position. A point set is convex or in convex position if it determines a convex polygon. A convex subset Q of P is said to be empty if no point of P lies inside the convex hull of Q. An empty convex subset of P with k elements is also called a k-hole of P . Let P be an n planar point set in general position. For a subset Q of P , denote the area of the convex hull of Q by A(Q). In [3], we considered the ratio between the maximum area of 3-holes (empty triangles) T of P and the whole area A(P ). Namely, let