柯西不等式的再推广

FURTHER GENERALIZATION OF CAUCHY-INEQUALITY

CallebautDK于六十年代将柯西不等式推广为 ni =1aαib2 -αi ni =1a2 -αi bαi ≤ ni=1a2 i ni=1b2 i 的形式 .该文把如上结果进一步推广至优化向量指数的情况 .

In this paper, we further generalize Cauchy_inequality, which Callebaut D K has improved to the form (ni=1a α ib θ-α i)(ni=1a θ-α ib α i)≤(ni=1a θ i)(ni=1b θ i). Our results deal with inequalities with superior vector exponents (Th2 and Th3).