Alonso Gutiérrez, DavidGonzález Merino, BernardoJiménez Gómez, Carlos Hugo2016-10-032016-10-032015-04-01Alonso Gutiérrez, D., González Merino, B. y Jiménez Gómez, C.H. (2015). Volume inequalities for the i-th-convolution bodies. Journal of Mathematical Analysis and Applications, 424 (1), 385-401.0022-247Xhttp://hdl.handle.net/11441/46756We obtain a new extension of Rogers-Sephard 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.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Mixed volumesConvolution bodiesinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1016/j.jmaa.2014.11.033