## Banach Journal of Mathematical Analysis

- Banach J. Math. Anal.
- Volume 5, Number 1 (2011), 19-28.

### On a Jensen-Mercer operator inequality

A. Ivelic, A. Matkovic, and J. E. Pecaric

#### Abstract

A general formulation of the Jensen-Mercer operator inequality for operator convex functions, continuous fields of operators and unital fields of positive linear mappings is given. As consequences, a global upper bound for Jensen's operator functional and some properties of the quasi-arithmetic operator means and quasi-arithmetic operator means of Mercer's type are obtained.

#### Article information

**Source**

Banach J. Math. Anal., Volume 5, Number 1 (2011), 19-28.

**Dates**

First available in Project Euclid: 14 August 2011

**Permanent link to this document**

https://projecteuclid.org/euclid.bjma/1313362976

**Digital Object Identifier**

doi:10.15352/bjma/1313362976

**Mathematical Reviews number (MathSciNet)**

MR2738516

**Zentralblatt MATH identifier**

1221.47031

**Subjects**

Primary: 47A63: Operator inequalities

Secondary: 47A64: Operator means, shorted operators, etc.

**Keywords**

Jensen--Mercer operator inequality operator convex functions continuous fields of operators Jensen's operator functional quasi-arithmetic operator means

#### Citation

Ivelic, A.; Matkovic, A.; Pecaric, J. E. On a Jensen-Mercer operator inequality. Banach J. Math. Anal. 5 (2011), no. 1, 19--28. doi:10.15352/bjma/1313362976. https://projecteuclid.org/euclid.bjma/1313362976