An inequality similar to the entropy inequality

WU JiMei;HUANG JinYang

Journal of Beijing University of Chemical Technology ›› 2013, Vol. 40 ›› Issue (增刊) : 109-111.

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Journal of Beijing University of Chemical Technology ›› 2013, Vol. 40 ›› Issue (增刊) : 109-111.
管理与数理科学

An inequality similar to the entropy inequality

  • WU JiMei;HUANG JinYang
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Abstract

The information entropy inequality describes an important property of the information entropy, namely, nonnegativity of the relative entropy. An inequality similar to the entropy inequality is proposed, and for the case of the variable number n=3, it is proved that the inequality a1a1+a2a2+a3a3≥a1x1+a2x2+a3x3 is true under the conditions 0<a1≤a2≤a3, a1≤xi≤a3(i=1,2,3) and x1+x2+x3=a1+a2+a3, and the equality holds if and only if x1=a1,x2=a2,x3=a3.

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WU JiMei;HUANG JinYang. An inequality similar to the entropy inequality[J]. Journal of Beijing University of Chemical Technology, 2013, 40(增刊): 109-111

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