Jensen类二重积分不等式的改进  

Improved Jensen Like Inequality with Double Integral

作　　者：张海洋[1,2] 熊良林[3,1] 吴涛[1] 李永昆[3] 

机构地区：[1]云南民族大学数学与计算机科学学院,云南昆明650500 [2]南京理工大学理学院,江苏南京210094 [3]云南大学数学与统计学院,云南昆明650091

出　　处：《云南师范大学学报（自然科学版）》2016年第5期21-26,共6页Journal of Yunnan Normal University:Natural Sciences Edition

基　　金：国家自然科学基金资助项目(11461082;11601474)

摘　　要：对一类Jensen类二重积分不等式进行了改进,在改进的新不等式中,被积函数为含有导数的二次型函数.首先采用新的函数构造方法,给出了原有Jensen类不等式的较为简洁的证明.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、优越性和保守性.This article mainly studied the improvement problem of Jensen like inequality with double integral. The integrand function in the new inequality we improved is a quadratic function including derivative. Firstly,the more concise and clear proof methods is provided through apply- ing a novel construction method of functions on the proof of this type of existing Jensen inequal- ity in this article. Secondly,based on the above method of proof,a new type Jensen like inequality with double integral is derived by combining with free matrix thought and calculating technics of integral inequality. Finally,the reasonability,superiority and less conservative of the proposed new inequalities are analyzed theoretically.

关 键 词：Jensen类不等式 函数构造法 二重积分不等式 

分 类 号：O172.2[理学—数学]