Skip to main content
Log in

Further Refinements of the Generalized Reverse of Young’s Inequality

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

The main goal of this article is to present some new refinements of an important generalized reverse of Young’s inequality due to J. Zhao [Results Math 77,8(2022)]. As applications, we prove some related inequalities for operators.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Data availability statement

My manuscript has no associate data.

References

  1. Al-Manasrah, Y., Kittaneh, F.: A generalization of two refined Young inequalities. Positivity 19, 757–768 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  2. Al-Manasrah, Y., Kittaneh, F.: Further generalization, refinements and reverses of the Young and Heinz inequalities. Results, Math. 19, 757–768 (2016)

    MATH  Google Scholar 

  3. Choi, D.: A generalization of Young-type inequalities. Math. Inequalities Appl. 21, 99–106 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  4. Furuichi, S.: On refined Young inequalities and reverse inequalities. J. Math. Inequal. 5, 21–30 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Hirzallah, O., Kittaneh, F.: Matrix Young inequalities for the Hilbert-Schmidt norm. Linear Algebra Appl. 308, 77–84 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ighachane, M.A., Akkouchi, M.: A new generalization of two refined Young inequalities and applications. Moroccan J. Pure Appl. Anal. 6(2), 155–167 (2020)

    Article  MATH  Google Scholar 

  7. Ighachane, M. A., Akkouchi, M., Benabdi, El Hassan.: A new generalized refinement of the weighted arithmetic-geometric mean inequality, Math. Ineq. Appl. 23(3), 1079–1085 (2020)

  8. Ighachane, M.A., Akkouchi, M.: Further generalized refinement of Yong’s inequalities for \(\tau \)-measurable operators. Moroccan J. Pure and Appl. Anal. 7(2), 214–226 (2021)

    Article  Google Scholar 

  9. Ighachane, M.A., Akkouchi, M.: A generalized refinement of Yonng’s inequality and applications. Appl. Math. E-Note 21, 129–138 (2021)

    MATH  Google Scholar 

  10. Ighachane, M.A., Akkouchi, M.: A new generalized refinement of Young’s inequality and applications. J. Math. Ineq. 15(3), 1019–1029 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  11. Ighachane, M.A., Akkouchi, M.: A new generalization of refined Young inequalities for \(\tau \)-measurable operators. Filomat. 35(4), 1253–1265 (2021)

    Article  MathSciNet  Google Scholar 

  12. Ighachane, M. A., Akkouchi, M.: Further refinement of Young’s type inequality for positive linear maps, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, (2021), https://doi.org/10.1007/s13398-021-00032-4

  13. Kittaneh, F., Al-Manasrah, Y.: Improved Young and Heinz inequalities for matrices. J. Math. Anal. Appl 36, 292–269 (2010)

    MathSciNet  MATH  Google Scholar 

  14. Kittaneh, F., Al-Manasrah, Y.: Reverse Young and Heinz inequalities for matrices. Linear Multilinear Algebra 59, 1031–1037 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  15. Kubo, F., Ando, T.: Means of positive operators, Math Ann. 246(3):205–224 (1979/1980)

  16. Sababheh, M.: Graph indices via the AM-GM inequality. Discrete Appl. Math. 230(4), 100–111 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  17. Pečarić, J., Furuta, T., Mićić, T., Seo, T.: Mond-Pečarić Method in Operator Inequalities. Element, Zagreb (2005)

    MATH  Google Scholar 

  18. Zhao, J.: Some refinements of the improved Young and its reverse Inequalities, Results. Math 77, Article number: 8 (2022). https://doi.org/10.1007/s00025-021-01525-z

Download references

Acknowledgements

The author is grateful to the anonymous referees and editor’s for their valuable comments and helpful suggestions, which led to a great improvement of this paper.

Funding

The authors have not disclosed any funding.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mohamed Amine Ighachane.

Ethics declarations

Conflict of interest

The authors have not disclosed any competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ighachane, M.A. Further Refinements of the Generalized Reverse of Young’s Inequality. Results Math 77, 214 (2022). https://doi.org/10.1007/s00025-022-01747-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00025-022-01747-9

Keywords

Mathematics Subject Classification

Navigation