英语翻译翻译内容是：摘要：平均值不等式在不等式理论中处于核心地位,是数学中最重要的基本不等式之一,因此,它在数学的很多领

Average value inequality is at the core position in the theory of inequality,is one of the most important basic inequalities in mathematics,therefore,in many fields of mathematics have broad application.This paper simply introduces the method to prove inequality of several representative,including the backward induction,method,probability inequalities proof,and summarizes its application in various aspects of function and equation,analytic geometry,plane geometry,solid geometry inequality,triangle inequality problem and the triangle inequality,extremum problems,sequence and limit.Provides convenience for future study ofthis problem,help to solve other inequalities proof.