[Banach] Abstract of a paper by Deping Ye

This is an announcement for the paper "Inequalities for general mixed affine surface areas" by Deping Ye. Abstract: Several general mixed affine surface areas are introduced. We prove some important properties, such as, affine invariance, for these general mixed affine surface areas. We also establish new Alexandrov-Fenchel type inequalities, Santal\'{o}-type inequalities, and affine isoperimetric inequalities for these general mixed affine surface areas. Archive classification: math.MG math.FA Mathematics Subject Classification: 52A20, 53A15 Submitted from: deping.ye@gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1112.5129 or http://arXiv.org/abs/1112.5129