Continuos quantitative Helly-type results

Brazitikos' results on quantititative Helly-type theorems (for the volume and for the diameter) rely on the work of Srivastava on approximate John's decompositions with few vectors. We change this technique by a stronger recent result due to Friedland and Youssef that allow us to obtain Helly-type versions which are sensitive to the number of convex sets involved.