Abstract
In this paper, we define the \(L_p\)-mixed affine surface area probability measure and obtain the log-Minkowski inequalities for nonsymmetric convex bodies of \(L_p\)-mixed affine surface area. Besides, we also establish the functional inequalities for \(L_p\)-mixed affine surface area, which are more general form than the log-Minkowski inequalities of \(L_p\)-mixed affine surface area.