The main purpose of the present article is to introduce a new concept and call it Orlicz mixed geominimal surface area \(G_{\varphi }(K_{1},\ldots ,K_{n})\) of n convex bodies \(K_{1},\ldots ,K_{n}\) , which obeys classical basic properties. The new affine geometric quantity in special case yields Petty’s geominimal surface area G(K), Lutwak’s p-geominimal surface area \(G_{p}(K)\) and the newly established Orlicz geominimal surface area \(G_{\varphi }(K)\) . The Orlicz mixed geominimal surface area inequality is established, which in special case yields Petty’s geominimal surface area inequality, Lutwak’s p-geominimal surface area inequality and Orlicz geominimal surface area inequality, respectively. Moreover, the related concepts and inequalities of \(L_{p}\) -mixed geominimal surface area are also derived here.
