若干重要积分不等式的等价性  

On the Equivalence between Some Integral Inequalities

作　　者：郝金彪[1] 吕巍[1] 

机构地区：[1]辽宁师范大学数学系,辽宁大连116029

出　　处：《辽宁师范大学学报（自然科学版）》2003年第3期240-243,共4页Journal of Liaoning Normal University:Natural Science Edition

摘　　要：给出了几何平均值与算术平均值不等式、cauchy不等式、Чебышев(切比雪夫)不等式、Н lder不等式、Ляпунов(利雅普诺夫)不等式、三角不等式和Minkowski不等式的积分形式并证明了它们之间的等价性,证明了它们τ2(x)dx>0,其中τ(x)是区间[a,b]上任一正值连续函数.The inequalities, inequality G(a)≤A(a), cauchy inequality, Tchebychef inequality, Lyapunov inequality, нёlder inequality, triangle inequality and Minkowski inequality,are given and their equivalence are proved.We have proved that they are all equivalent to ∫baτ2(x)dx>0.

关 键 词：积分不等式 等价性 几何平均值不等式 算术平均值不等式 CAUCHY不等式 切比雪夫不等式 HOELDER不等式 

分 类 号：O178[理学—数学]