摘要
利用提升维度的方法并结合几何图形直观分析,给出一道一元函数积分均值不等式的新证明,并将原不等式推广至形式较为对称的不等式,使得原不等式成为新不等式的特例.最后证明新不等式与函数单调递减的定义等价.
A new proof of an integral mean value inequality is given by lifting the dimension of the variable space. The original inequality is generalized to a new inequality in a symmetry form. It is proved also that the new inequality is equivalent to the decreasingness of＇the related function.
出处
《高等数学研究》
2011年第2期20-21,30,共3页
Studies in College Mathematics
基金
上海高校选拔培养优秀青年教师科研专项基金
关键词
积分均值
积分不等式
单调递减函数.
integral mean value, integral inequality, monotone decreasing function
