The Inequalities Involving Jensen Functions
涉及Jensen函数的不等式

The concepts of Jensen function and Jensen mean are introduced.By means of mathematical and algebraic tools,the factoring formula of Jensen functions is obtained. Using this formula,a brand-new idea for strengthened and generalized Jensen's inequality is also given.As an application,we give a sufficient condition under which Jensen's inequality holds.Our aim is to provide some useful analytical inequalities for mathematics research.