In this paper, we establish an affine Orlicz log-Minkowki inequality for the affine quermassintegrals by introducing new concepts of affine measures and Orlicz mixed affine measures, and using the newly established Orlicz affine Minkowski inequality for the affine quermassintegrals. The affine Orlicz log-Minkowski inequality in special case yields L_{p}-affine log-Minkowski inequality. The affine log-Minkowski inequality is also derived.



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 Zhao, Chang-Jian