Sharp bounds for the difference between the arithmetic and geometric means

被引:8
作者
Aldaz, J. M. [1 ]
机构
[1] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain
关键词
Variance; Arithmetic-geometric inequality; INEQUALITY; REFINEMENT; VERSION;
D O I
10.1007/s00013-012-0434-7
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We present sharp bounds for in terms of the variance of the vector .
引用
收藏
页码:393 / 399
页数:7
相关论文
共 11 条
[1]   A stability version of Holder's inequality [J].
Aldaz, J. M. .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 343 (02) :842-852
[2]   COMPARISON OF DIFFERENCES BETWEEN ARITHMETIC AND GEOMETRIC MEANS [J].
Aldaz, J. M. .
TAMKANG JOURNAL OF MATHEMATICS, 2011, 42 (04) :453-462
[3]   A MEASURE-THEORETIC VERSION OF THE DRAGOMIR-JENSEN INEQUALITY [J].
Aldaz, J. M. .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2012, 140 (07) :2391-2399
[4]  
Aldaz JM, 2009, J MATH INEQUAL, V3, P213
[5]   Concentration of the Ratio between the Geometric and Arithmetic Means [J].
Aldaz, J. M. .
JOURNAL OF THEORETICAL PROBABILITY, 2010, 23 (02) :498-508
[6]  
Aldaz J.M., 2008, J. Math. Ineq. Appl, V2, P473, DOI DOI 10.7153/JMI-02-42
[7]   A new refinement of the arithmetic mean-geometric mean inequality [J].
Alzer, H .
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1997, 27 (03) :663-667
[8]   REFINEMENT OF ARITHMETIC MEAN GEOMETRIC MEAN INEQUALITY [J].
CARTWRIGHT, DI ;
FIELD, MJ .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1978, 71 (01) :36-38
[9]   Bounds for the normalised Jensen functional [J].
Dragomir, Sever S. .
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2006, 74 (03) :471-478
[10]   ON REFINED YOUNG INEQUALITIES AND REVERSE INEQUALITIES [J].
Furuichi, Shigeru .
JOURNAL OF MATHEMATICAL INEQUALITIES, 2011, 5 (01) :21-31