Some recent results about Jensen's operator inequality and its converses with application to operator means

Mićić Hot, Jadranka (2010) Some recent results about Jensen's operator inequality and its converses with application to operator means. = Some recent results about Jensen's operator inequality and its converses with application to operator means. In: International Conference on Mathematical Inequalities and Applications 2010 (MIA 2010), 07-13.03.2010., Lahore; Pakistan.

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Abstract

The goal of this lecture is to present a generalization of Jensen's operator inequality and its converses for fields of positive linear mappings such that is not unital. First we give general formulations of Jensen's operator inequality and it's converses. As a consequence, difference and ratio type of converses of Jensen's operator inequality are obtained. In addition, we discuss the order among quasi-arithmetic means in a general setting. As an application we get some comparison theorems for power functions and power means. Also we give the chaotic order version of these results.

Item Type: Conference or Workshop Item (Lecture)
Keywords (Croatian): Jensen's inequality; converses of Jensen's inequality; Mond-Pecaric method; quasi-arithmetic mean; power mean
Subjects: NATURAL SCIENCES > Mathematics
TECHNICAL SCIENCE > Electrical Engineering
Divisions: 1500 Chair of Mathematics
Indexed in Web of Science: No
Indexed in Current Contents: No
Date Deposited: 03 Jul 2015 12:37
Last Modified: 23 May 2017 11:26
URI: http://repozitorij.fsb.hr/id/eprint/4424

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