The well-known majorizing inequality is generalized to space of higher dimensions, and a important majorizing inequality is obtained. The concept of generalized convex function of several variables is introduced. A material criterion is given. As applications of majorizing inequality of convex function of several variables, some majorizing inequalities of eigenvalue and singular value of matrix are obtained.
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杨定华. 广义多元凸函数与控制不等式(Ⅰ)[J]. 科学技术与工程, 2005, (21): 1581-15851589. YANG Dinghua. The Generalized Convex Function of Several Variables and Majorizing Inequalities(Ⅰ)[J]. Science Technology and Engineering,2005,(21):1581-15851589.