Hadamard Inequalities Of Convex Function And Their Applications

Inequalities related to convex function play a very important role in the basic theory and application of mathematics. In 1893, of the Jensen convex function definition Hadamard gave the classic inequalities Hadamard inequality. Hadamard inequality was developed along with convex function. It is very important for theoretical and applied of convex function. The fact that the convexity of convex function and its definition is based on inequality makes convex function become a very important tool to prove inequality so that a lot of inequalities were established, reformed and extended. And the reform, refinement, expansion, extension and application of Hadamard inequality of convex function have become a hot research issue for mathematicians.In the first part of this paper, we introduced the research background and some previous work of Hadamard inequality for convex function. On the base of previous work, we propose main research direction in this paper.According to the premise of [17][20] and the second part of the paper, the third part of the paper establish two mappings about one definite integral of Hadamard inequality. Also, on the base of [20], we establish three mappings about multiple integral of Hadamard inequality. We investigate the mappings properties, discover some new convex functions and some new inequalities.Finally, this paper gives some applications of Hadamard inequality, also gets some new inequalities.This paper enriches Hadamard inequality and will play a certain role in promoting the developments of the Hadamard inequality.