The Inequality Proofs and Applications of Function’s Strict Convexity

Hongheng Yin1, Yan Li1,2

1School of Applied Mathematics, Beijing Normal University, Zhuhai, 519087, China

2College of Mathematics and Information Science, Hebei University, Baoding, 071002, China

Abstract: Convexity is an important property of functions, which has many applications in geometry, function optimization, economics, and other problems. In this paper, we mainly study and prove some theorems and properties about strictly convex functions and use examples to illustrate the importance of these results. The proofs of these theorems provide a theoretical basis of solving problems about strict inequalities of the strictly convex functions.

Keywords: Strictly convex function; Strict Jensen's inequality; Strictly convex application