【摘要】 不等式是研究分析数学的重要工具,很多常见不等式又是与函数的凸性分不开的 本文根据Jensen不等式,运用简捷的初等方法和恒等变形的技巧,导出一些重要不等式,再由凹函数f(x)=xα-αx(x>0,0<α<1)直接导出Young不等式更多还原

【Abstract】 Inequality is an important tool to research analytical mathematies, and a lot of common inequality can not be separated from the convex quality of function. Here, based on Jensen Inequality, with the basic method of elementary equality and the variation of identical equation, some important inequalites. Then from concave function f(x)=x~α-αx(x>0, 0<α<1), the Young Inequality was deduced directly更多还原