Some complementary inequalities to Jensen's operator inequality

Jadranka Mićić; Hamid Reza Moradi; Shigeru Furuichi

doi:10.1186/s13660-018-1616-z

Some complementary inequalities to Jensen's operator inequality

J Inequal Appl. 2018;2018(1):25. doi: 10.1186/s13660-018-1616-z. Epub 2018 Jan 25.

Authors

Jadranka Mićić¹, Hamid Reza Moradi², Shigeru Furuichi³

Affiliations

¹ 1Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb, Croatia.
² 2Young Researchers and Elite Club, Mashhad Branch, Islamic Azad University, Mashhad, Iran.
³ 3Department of Information Science, College of Humanities and Sciences, Nihon University, Tokyo, Japan.

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