Convex combinations, barycenters and convex functions

Journal of inequalities and applications

Zlatko Pavić¹ 

关键词: convex combination;    barycenter;    convex function;    Jensen’s inequality;    quasi-arithmetic mean;   

DOI  :  10.1186/1029-242X-2013-61

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The article first shows one alternative definition of convexity in the discrete case. The correlation between barycenters, Jensen’s inequality and convexity is studied in the integral case. The Hermite-Hadamard inequality is also obtained as a consequence of a concept of barycenters. Some derived results are applied to the quasi-arithmetic means and especially to the power means. MSC:26A51, 26D15, 28A10, 28A25.

【 授权许可】

CC BY