engleski

An interpolation of Jensen's inequality and its applications to mean inequalities

In this paper, we show operator versions of the inequality due to Cho, Matic and Pecaric in connection to Jensen’s inequality for convex functions. As applications, we obtain an interpolation of the weighted arithmetic- geometric mean inequality for the Karcher mean of positive invertible operators on a Hilbert space. Moreover, we obtain an interpolation between the quasi-arithmetic means.

Jensen’s inequality ; positive linear map ; convex function ; Karcher mean ; quasiarithmetic mean

The second author is partially supported by the Ministry of Education, Science, Sports and Culture, Grant- in-Aid for Scientific Research (C), JSPS KAKENHI Grant Number JP 16K05253.