engleski

Some complementary inequalities to Jensen's operator inequality

In this paper, we study some complementary inequalities to Jensen’s inequality for self- adjoint operators, unital positive linear mappings, and real valued twice differentiable functions. New improved complementary nequalities are presented by using an improvement of the Mond-Pečarić method. These results are applied to obtain some inequalities with quasi-arithmetic means

self-adjoint operator ; positive linear mapping ; convex function ; converse of Jensen's operator inequality ; Mond-Pečarić method

The third author was partially supported by JSPS KAKENHI Grant Number 16K05257.