Application of Convex Functions and Jensen Inequality

摘要

Functions are the important fundamental concepts in mathematics and the key research object in mathematical analysis. Convex function is a class of very important functions which is widely used in pure mathematics, functional analysis, optimization theory, mathematical economics. This paper firstly introduces a definition of convex function, and then gives properties of convex function and its judging theorem, finally, gives examples which show how to prove more complex inequalities using Jensen inequality of discrete form.