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Monatshefte für Mathematik

, Volume 181, Issue 1, pp 187–203 | Cite as

Hermite–Hadamard type inequalities for operator geometrically convex functions

  • A. Taghavi
  • V. DarvishEmail author
  • H. M. Nazari
  • S. S. Dragomir
Article

Abstract

In this paper, we introduce the concept of operator geometrically convex functions for positive linear operators and prove some Hermite–Hadamard type inequalities for these functions. As applications, we obtain trace inequalities for operators which give some refinements of previous results.

Keywords

Hermite–Hadamard inequality Operator geometrically convex function Trace inequality Unitarily invariant norm 

Mathematics Subject Classification

47A63 15A60 47B05 47B10 26D15 

Notes

Acknowledgments

This work was written whilst the second author was visiting Victoria University during his short sabbatical leave provided by the Ministry of Science, Research and Technology. He thanks them for the support and hospitality.

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Copyright information

© Springer-Verlag Wien 2015

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Mathematical SciencesUniversity of MazandaranBabolsarIran
  2. 2.Mathematics, School of Engineering and ScienceVictoria UniversityMelbourneAustralia

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