摘要
借助于基本不等式,本文推广了文[1-4]的部分结果,统一了 Beckenbach不等式与别的不等式,(如 Minkowski 不等式等.)
In this paper,Beckenbach's inequality [1] is generalized as follows: Theorem Let the values(a)≡(a_1,a_2,…,a_n)and(b)≡(b_1,b_2,…,b_n)be positive,and t≥1,p≥1≥r.Then [M_p(a+b)]~t/[m_r(a+b)]^(t-1)≤([M_p(a)]~t/[M_r(a)]^(t-1))+([M_p(b)]~t/[M_r(b)]^(t-1)) The inequality is reversed for 0≤t≤1,p≤1≥r. In particular,some inequalities of [1-4] are the consequences of the above theorem.
关键词
不等式
贝肯巴赫
闵可夫斯基
卓斜
Beckenbach's inequality
Minkowski's inequality
Dresher's inequality
