doi:10.1016/j.jmaa.2014.11.033engAlonso Gutiérrez, DavidGonzález, BernardoJiménez, Carlos HugoVolume inequalitites for the i-th convolution bodiesART-2015-97163We obtain a new extension of Rogers–Shephard inequality providing an upper bound for the volume of the sum of two convex bodies K and L. We also give lower bounds for the volume of the k-th limiting convolution body of two convex bodies K and L. Special attention is paid to the (n - 1)-th limiting convolution body, for which a sharp inequality, which is equality only when K = -L is a simplex, is given. Since the n-th limiting convolution body of K and -K is the polar projection body of K, these inequalities can be viewed as an extension of Zhang’s inequality.2015http://zaguan.unizar.es/record/5793510.1016/j.jmaa.2014.11.033http://zaguan.unizar.es/record/57935oai:zaguan.unizar.es:57935info:eu-repo/grantAgreement/ES/MICINN/MTM2009-10418info:eu-repo/grantAgreement/ES/MICINN/MTM2010-16679JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 424 (2015), 385-401byhttp://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccess