积分不等式证明中的辅助函数方法

Auxiliary Function Method in Proof of Integral Inequality

不等式在数学研究和实际中有广泛应用,本文分析了大学生数学竞赛赛题中出现的有关不等式证明问题,基于构造辅助函数方法和柯西中值定理建立了更一般的积分不等式,推广和改进了大学生数学竞赛赛题中的不等式和已有文献中的不等式.

Inequalities are widely used in mathematical research and practice. This paper analyses the problems of proving inequalities in the Undergraduate s Mathematical Contest. Based on the method of constructing auxiliary functions and Cauchy s mean value theorem, more general integral inequalities are established, which generalize the inequalities appearing in Undergraduate s Mathematical Contest and the inequalities in the existing literature.