【摘要】 引入了Jensen函数及Jensen平均的概念,借助于数学分析和代数工具给出了Jensen函数的分解公式,利用这个公式给出了推广和加强Jensen不等式的一种崭新的思路,作为应用,给出了Jensen不等式成立的一个有趣的充分条件．旨在为数学研究提供一些有用的解析不等式．更多还原

【Abstract】 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.更多还原