A refinement of the integral form of Jensen’s inequality

Journal of inequalities and applications

Lá¹ 

关键词: Jensen’s inequality;    convex function;    measure space;    Hermite-Hadamard inequality;   

DOI  :  10.1186/1029-242X-2012-178

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

There are a lot of refinements of the discrete Jensen’s inequality, and this problem has been studied by many authors. It is also a natural problem to give analogous results for the classical Jensen’s inequality. In spite of this, few papers have been published dealing with this problem. The purpose of this paper is to give some refinements of the classical Jensen’s inequality. The results give a new approach of this topic. Moreover, new discrete inequalities can be derived, and the integral analogous of discrete inequalities can be obtained. We also have new refinements of the left-hand side of the Hermite-Hadamard inequality. MSC:26D07, 26A51.

【 授权许可】

CC BY