Key points are not available for this paper at this time.
Two of the most important affine isoperimetric inequalities are the Blaschke-Santalo inequality (see, e.g., Gardner 6, p. 322 or Schneider 12, p. 425) and the classical affine isoperimetric inequality of affine differential geometry (see, e.g., Schneider 12, p. 419). These two inequalities are closely related in that given either one of these inequalities, then by well-known methods one can be quickly deduced from the other. The aim of this article is to establish a new family of analytic inequalities and their geometric counterparts. One of the members of this family of inequalities turns out to be the Blaschke-Santalo inequality.
Lutwak et al. (Wed,) studied this question.