SOME REVERSES OF THE JENSEN INEQUALITY WITH APPLICATIONS

被引：25
作者：
Dragomir, S. S. [1 ,2 ]
机构：
[1] Victoria Univ, Sch Sci & Engn, Melbourne, MC 8001, Australia
[2] Univ Witwatersrand, Sch Computat & Appl Math, ZA-2050 Johannesburg, South Africa
来源：
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2013年 / 87卷 / 02期
关键词：
Jensen's inequality; Holder's inequality; measurable functions; Lebesgue integral; divergence measures; f-divergence measures; DIVERGENCE; COEFFICIENTS; PROBABILITY; SELECTION; BOUNDS;
D O I：
10.1017/S0004972712001098
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Two new reverses of the celebrated Jensen's inequality for convex functions in the general setting of the Lebesgue integral, with applications to means, Holder's inequality and f-divergence measures in information theory, are given.
引用
收藏
页码：177 / 194
页数：18
相关论文
共 39 条
[1]  
ALI SM, 1966, J ROY STAT SOC B, V28, P131
[2]  
[Anonymous], 1972, STAT DECOMPOSITION A
[3]  
[Anonymous], 1989, Theory of Statistical Inference and Information
[4]  
[Anonymous], 1943, Bull Calcutta Math Soc, DOI DOI 10.1038/157869B0
[5]  
[Anonymous], 1967, IEEE T INFORM THEORY, DOI DOI 10.1109/TIT.1967.1054013
[6]  
[Anonymous], 1981, Information Theory: Coding Theorems for Discrete Memoryless Systems
[7]   F-ENTROPIES, PROBABILITY OF ERROR, AND FEATURE SELECTION [J].
BENBASSAT, M .
INFORMATION AND CONTROL, 1978, 39 (03) :227-242
[8]  
Burbea I., 1982, IEEE T INFORM THEORY, V28, P489
[9]  
Chen C.H., 1973, STAT PATTERN RECOGNI
[10]   APPROXIMATING DISCRETE PROBABILITY DISTRIBUTIONS WITH DEPENDENCE TREES [J].
CHOW, CK ;
LIU, CN .
IEEE TRANSACTIONS ON INFORMATION THEORY, 1968, 14 (03) :462-+
1234