Orlicz mixed width measures

In this paper, we establish the Orlicz logarithmic Minkowski inequality for the width integrals by introducing the new {\it Orlicz mixed width measures} and using the newly established Orlicz mixed width inequality. The Orlicz width logarithmic Minkowski inequality in special case yields the width logarithmic Minkowski inequality and the $L_{p}$-width logarithmic Minkowski inequality, respectively.