Studing Jensen’s Inequality form Easy to Hard in Mathematical Analysis

The proof of inequality is always the key and difficult points in the teaching of mathematical analysis. The use of Jensen inequality can make the proof of inequality simple and clear. The current textbooks of mathematical analysis are not unified in expounding and proof of the Jensen inequalities. Through a systematic study of discrete and integral Jensen inequalities from easy to hard, by use of the property of convex function, a unified and simplified method is worked out to prove several types of Jensen inequalities.