A Generalized Affine Isoperimetric Inequality
  A purely analytic proof is given for an inequality that has as a direct consequence the two most important affine isoperimetric inequalities of plane convex geometry: The Blaschke-Santalo inequality and the affine isoperimetric inequality of affine differential geometry. 
Wenxiong Chen, Ralph Howard, Erwin Lutwak, Deane Yang, Gaoyong Zhang