Journal of Inequalities and Applications (Jan 2011)
A new interpretation of Jensen's inequality and geometric properties of <b> <it>φ</it> </b>-means
Abstract
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 Mφ (f). We first give a new interpretation of Jensen's inequality by φ-mean. Next, as an application, we consider some geometric properties of Mφ (f), for example, refinement, strictly monotone increasing (continuous) φ-mean path, convexity, etc. Mathematics Subject Classification (2000): Primary 26E60; Secondary 26B25, 26B05.
