A new interpretation of Jensen's inequality and geometric properties of φ -means

Journal of Inequalities and Applications

关键词: Jensen's inequality;    Mean;    Refinement;    Convexity;    Concavity;   

DOI  :  

来源: DOAJ

【 摘 要 】

Abstract

We introduce a mean of a real-valued measurable function f on a probability space induced by a strictly monotone function φ. Such a mean is called a φ-mean of f and written by M_φ (f). We first give a new interpretation of Jensen's inequality by φ-mean. Next, as an application, we consider some geometric properties of M_φ (f), for example, refinement, strictly monotone increasing (continuous) φ-mean path, convexity, etc.

Mathematics Subject Classification (2000): Primary 26E60; Secondary 26B25, 26B05.

【 授权许可】

Unknown