Some complementary inequalities to Jensen’s operator inequality

Abstract

Abstract 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 inequalities are presented by using an improvement of the Mond-Pečarić method. These results are applied to obtain some inequalities with quasi-arithmetic means.

Keywords

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