More accurate classes of jensen–type inequalities for convex and operator convex functions

Motivated by a recent refinement of the scalar Jensen inequality obtained via linear interpolation, in this paper we develop a general method for improving two classes of Jensen-type inequalities for bounded self-adjoint operators. The first class refers to a usual convexity, while the second one deals with the operator convexity. The general results are then applied to quasi-arithmetic and power operator means. As a consequence, we obtain strengthened forms of the inequalities between arithmetic, geometric and harmonic operator means. We also obtain more accurate Young-type inequalities for unitarily invariant norms as well as more precise relations for some important jointly concave mappings.

Авторы
Choi D.1 , Krni M. 2, 4 , Peari J.3
Издательство
Element D.O.O.
Номер выпуска
2
Язык
Английский
Страницы
301-321
Статус
Опубликовано
Том
21
Год
2018
Организации
  • 1 Southern Illinois University, Edwardsville Department of Mathematics and Statistics, Box 1653, Edwardsville, IL 62026, United States
  • 2 University of Zagreb, Faculty of Electrical Engineering and Computing, Unska 3, Zagreb, 10000, Croatia
  • 3 University of Zagreb, Faculty of Textile Technology, Prilaz baruna Filipovi?a 28a, Zagreb, 10000, Croatia
  • 4 RUDN University, Miklukho-Maklaya str. 6, Moscow, 117198, Russian Federation
Ключевые слова
Convexity; Jensen inequality; Operator convexity; Operator mean; Refinement; Young inequality
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/6753/