新的Jensen类二重积分不等式的改进

A new improved Jensen like inequality with double integral

研究一类Jensen类二重积分不等式的改进问题.在改进的新不等式中,被积函数为不含有导数的二次型函数.首先,采用函数构造方法,为现有的该类型Jensen不等式给出了一种较为简洁的证明.然后,基于上述证明方法,结合自由矩阵思想和积分运算技巧,得到一类新的Jensen类二重积分不等式.最后,从理论上分析了该新不等式的合理性、优越性和具有更低的保守性.

It＇ s studied the improvement problem of Jensen like inequality with double integral.The integrandfunction in the new inequality we improved is a quadratic function excluding derivative.Firstly, the more conciseand clear proof methods is provided through applying construction method of functions on the proof of this type ofexisting Jensen inequality in this article.Secondly,based on the above method of proof,a new type Jensen like in-equality with double integral is derived by combining with free matrix thought and calculating technics of integralinequality.Finally,the reasonability, superiority and less conservative of the proposed new inequalities are ana-lyzed theoretically.