摘要
分析了Jensen不等式的来胧去脉,指出,在Jensen基本不等式的形成过程中,渗透着观察、类比联想、归纳、猜想等思想方法;而由Jensen基本不等式中的均等性联想到非均等性,则导致了Jensen总和不等式的产生;由Jensen总和不等式中变量的离散性联想到变量的连续性,则导致Jensen积分不等式的发现。
The origin and developmant of Jensen inequality is analysed. It is pointed out that the mentality, such as observation, analogy association, induction, guess permeates through the course of forming Jensen basic inequa lity. Associating the disproporlionality from the proportionality in Jensen basic inequality leads to the generation of Jensen summation inequality. Associating the continuous variable from the discrete variable in Jensen summation inequality leads to the discovery of Jensen integral inequality.
出处
《曲阜师范大学学报（自然科学版）》
CAS
1993年第3期79-82,共4页
Journal of Qufu Normal University(Natural Science)
