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本文基于Brunn-Minkowski理论中宽度积分的研究，定义了Orlicz-log宽度积分，建立Orlicz-log宽度积分的Orlicz-Minkowski型不等式和Orlicz-Brunn-Minowski型不等式及它们间的等价关系。当φ(x,y)=x-p+y-p时，即为Lp-log宽度积分的Lp-Minkowski型不等式和Lp-Brunn-Minowski型不等式。
Abstract：Based on the study of width integral in Brunn-Minkowski theory, we define the Orlicz-log width integral and establish the Orlicz-Minowski type inequality and the Orlicz-Brunn-Minkowski type inequality of the Orlicz-log width integral as well as their equivalence relationship. When φ(x,y)=x-p+y-p is satisfied, the inequalities of Orlicz-log width integral is correspondingly transformed to Lp-Minowski type inequality and Lp-Brunn-Minkowski type inequality of Lp-log width integral.
[ 1 ] Schneider R.Convex Bodies:The Brunn-Minkowski Theory(Second expanded edition)[M].Cambridge:Cambridge Univ Press,2014.
[ 2 ] Lutwak E.A general Bieberbach inequality[J].Math Proc Gamb Phil Soc,1975,78:493-495.
[ 3 ] Lutwak E.Mixed width-integrals of convex bodies[J].Israel J Math,1977,28:249-253.
[ 4 ] Zhao C J.Orlicz version of the mixed width integrals[J].J Func Spaces,2018,2018:1-16.
[ 5 ] Firey W J.P-means of convex bodies[J].Math Scand,1962,10:17-24.
[ 6 ] Yuan J,Zhao L Z,Leng G S.Inequalities for Lp centroid body[J].Taiwan J Math,2007,13:1315-1325.
[ 7 ] Lu F,Leng G S.On Lp-Brunn-Minkowski type inequalities of convex bodies[J].Bol Soc Math Mexicana,2007,13:167-176.
[ 8 ] Lutwak E.The Brunn-Minkowski-Firey Theory I:Mixed volumes and the Minkowski Problem[J].J Differential Geom,1993,38:131-150.
[ 9 ] Wu D H,A generalization of Lp-Brunn-Minkowski inequalities and Lp-Minkowski problems for measures[J].Adv in Appl Math,2017,89:156-183.
[10] Feng Y B.General mixed width-integral of convex bodies[J].J Nonlinear Sci Appl,2016,9:4226-4234.
[11] Zhou Y.General Lp-mixed width-integral of convex bodies and related inequalities[J].Nonlinear Sci Appl,2017,10:4372-4380.
[12] Zhang X F,Wu S H.New Brunn-Minkowski type inequalities for general width-integral of index i[J].Wuhan Univ J Natural Sci,2019,24(06):474-478.
[13] Lai D D,Jin H L.The dual Brunn-Minkowski inequality for log-volume of star bodies[J].J Pure Appl Math,2005,36:177-188.
[14] Lutwak E,Yang D,Zhang G.Orlicz centroid bodies[J].J Differential Geom,2010,84(2):365-387.
[15] Gardner R,Hug D,Weil W.The Orlicz-Brunn-Minkowski theory:a general framework,additions,and inequalities[J].J Differential Geom,2014,97(3):427-476.
[16] Gardner R,Hug D,Weil W,et al.The dual Orlicz-Brunn-Minkowski theory[J].J Math Anal Appl,2015,430(2):810-829.
[17] Zhu B C,Zhou J Z,Xu W X.Dual Orlicz-Brunn-Minkowski theory[J].Adv in Math,2014,264:700-725.
[18] Hardy G,Littlewood J,Polya G.Inequalities[M].New York:Cambridge Univ Press,1952.
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DOI：
中图分类号:O186.5
引用信息:
[1]杨林,罗淼.Orlicz-log宽度积分的Orlicz-Brunn-Minowski型不等式[J].山东师范大学学报(自然科学版),2024,39(03):243-249.
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