Exponential convexity for Jensen’s inequality for norms

Journal of inequalities and applications

Julije Jakš¹ 

关键词: convex function;    exponentially convex function;    mean value theorems;    Stolarsky means;    26A24;    26A48;    26A51;    26D15;   

DOI  :  10.1186/s13660-016-1009-0

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we investigate n-exponential convexity and log-convexity using the positive functional defined as the difference of the left-hand side and right-hand side of the inequality from (Pečarić and Janić in Facta Univ., Ser. Math. Inform. 3:39-42, 1988). We also give mean value theorems of Lagrange and Cauchy types. Finally, we construct means with Stolarsky property.

【 授权许可】

CC BY