帮忙看看这段有没有语法或者拼写错误

帮忙看看这段有没有语法或者拼写错误Concavity-convexity of function is one of the essential of quality of function,it’s research on function have a very wide range of applications.And concave-convex function is a powerful tool to study and prove the inequality.This article firstly lists definition the concavity-convexity of function and obtains several of equivalent theorems to convex function.Then deduces some new properties and theorems of the convex function through proving the definitions,so as to obtain some distinctive methods of the convex function which are used very frequently.And derivation an important inequality of convexity — Jensen inequality,and obtain several of theorem to prove inequality.Moreover used the Jensen inequality proves to the Holder inequality,Cauchy inequality and other well-known inequality.Finally these conclusions will be applied to prove the inequality,so that they can make some complex inequality questions to be easily solved.And also using the convex function to prove inequality is more terse and ingenious than others.Some classical inequalities and some real life,production-related inequalities which are proved in this article provide the theory basis of structure some inequality question to the mathematics competition and the elementary mathematics.Meanwhile they have the interaction significance and reference value to people’s life.