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Acta Mathematica Vietnamica

, Volume 43, Issue 4, pp 607–618 | Cite as

Inequalities for Relative Operator Entropies and Operator Means

  • Shigeru Furuichi
  • Nicuşor Minculete
Article

Abstract

The main purpose of this article is to study estimates for the Tsallis relative operator entropy, by using the Hermite-Hadamard inequality. We obtain alternative bounds for the Tsallis relative operator entropy and in the process to derive these bounds, we established the significant relation between the Tsallis relative operator entropy and the generalized relative operator entropy. In addition, we study the properties on monotonicity for the weight of operator means and for the parameter of relative operator entropies.

Keywords

Operator inequality Positive operator Hermite-Hadamard inequality Operator mean Generalized relative operator entropy Tsallis relative operator entropy 

Mathematics Subject Classification (2010)

47A63 47A64 94A17 

Notes

Acknowledgements

The authors thank anonymous referees for giving valuable comments and suggestions to improve our manuscript.

Funding Information

The first author was partially supported by JSPS KAKENHI grant number 16K05257.

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of Information Science, College of Humanities and SciencesNihon UniversityTokyoJapan
  2. 2.Transilvania University of BraşovBraşovRomania

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