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Further improvements of Young inequality

  • Shigeru FuruichiEmail author
Original Paper

Abstract

We focus on the improvements for Young inequality. We give elementary proof for known results by Dragomir, and we give remarkable notes and some comparisons. Finally, we give new inequalities which are extensions and improvements for the inequalities shown by Dragomir.

Keyword

Young inequality and operator inequality 

Mathematics Subject Classification

26D07 26D20 and 15A45 

Notes

Acknowledgements

The author was partially supported by JSPS KAKENHI Grant Number 16K05257.

References

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    Dragomir, S.S.: A note on Young’s inequality. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A. Math. 111, 349–354 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
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    Dragomir, S.S.: On new refinements and reverse of Young’s operator inequality. arXiv:1510.01314v1
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    Furuichi, S., Minculete, N.: Alternative reverse inequalities for Young’s inequality. J. Math. Inequal. 5, 595–600 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
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    Zuo, H., Shi, G., Fujii, M.: Refined Young inequality with Kantorovich constant. J. Math. Inequal. 5, 551–556 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
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    Furuichi, S., Moradi, H.R.: Operator inequalities among arithmetic mean, geometric mean and harmonic mean. II. arXiv:1705.02185

Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Information Science, College of Humanities and SciencesNihon UniversityTokyoJapan

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