Jensen类一重积分不等式的改进

Improved Jensen-like inequality with single integral

主要研究了一类Jensen一重积分不等式的改进问题.其中,所研究的积分不等式的被积函数为不含导数的二次型函数.首先,采用新的函数构造方法,对现有改进的该类型Jensen不等式给出了一种较为简洁的证明方法.然后,基于上述证明方法,结合自由矩阵思想和积分不等式计算技巧,得到一类含有自由矩阵的新的Jensen类一重积分不等式.最后,从理论上分析了该新不等式的有效性、可行性、优越性和具有更低的保守性.

The improvement of Jensen-like inequality with single integral is studied in this paper. I t shows that the integrand function of the integral inequality is a quadratic function excluding derivatives. First of all, a more con-cise method is provided through applying a novel construction method of functions for the proof of this type of improved Jensens inequality. Then, based on the above method of proof, a new type of Jensen - like inequality with single integral which contain free matrices is derived by combining the free matrix approach with the calculating techniques of integral inequality. Finally, the effectiveness, feasibility, superiority and flexibility of the proposed new inequality are analyzed theoretically.