重要不等式之间的互相等价性  

On the Equivalence between Some Important Inequalities

作　　者：景占策[1] 

机构地区：[1]青海师范大学数学与信息科学系,青海西宁810008

出　　处：《湘南学院学报》2007年第5期19-23,共5页Journal of Xiangnan University

摘　　要：在实数集合的紧致性为已知的前提下,证明算术平均值与几何平均值不等式,Cauchy不等式,ЧeóыⅢeв不等式,Hlǒder不等式,三角不等式之间的互相等价性,而且它们都等价于一个实数的平方不小于零.In this paper it is shown that the basic inequality ,Cauchy inequality,Tchebychef inequality,Holder inequality,Lyapunov inequality, triangle inequality are all equivalent to the simple proposition that a^2≥0,,for every a∈R（set of real number）,provided the proposition that the closure of the set of rational number equals R is known.

关 键 词：不等式 实数集合的紧致性 不等式之间的等价性 

分 类 号：O122.3[理学—数学]