Article ID: MTJPAM-D-20-00014

Title: A New Refinement of Young’s Type Inequalities and Applications


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-20-00014; Volume 3 / Issue 2 / Year 2021, Pages 51-59

Document Type: Research Paper

Author(s): Mohamed Amine Ighachane a , Mohamed Akkouchi b

aDepartment of Mathematics, Faculty of Sciences-Semlalia, University Cadi Ayyad, Av. Prince My. Abdellah, BP: 2390, Marrakesh (40.000-Marrakech), Morocco (Maroc)

bDepartment of Mathematics, Faculty of Sciences-Semlalia, University Cadi Ayyad, Av. Prince My. Abdellah, BP: 2390, Marrakesh (40.000-Marrakech), Morocco (Maroc)

Received: 19 May 2020, Accepted: 11 May 2021, Published: 23 May 2021.

Corresponding Author: Mohamed Amine Ighachane (Email address: mohamedamineighachane@gmail.com)

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Abstract

In this paper, we present multiple-term refinements of Young’s type inequalities which extends and unifies two recent and important results due to L. Nasiri et al. (Int. J. Nonlinear Anal. Appl. 8, 261–267, 2017) and C. Yang et al. (Journal. Math. Inequalities 14, 401–419, 2020). As applications, we give some related inequalities for operators and matrices.

Keywords: Young’s type inequality, Operator inequality, Traces, Unitarily invariant norms

References:
  1. Y. Al- Manasrah and F. Kittaneh, A generalization of two refined Young inequalities, Positivity 19, 757–768, 2015.
  2. Y. Al- Manasrah and F. Kittaneh, Further generalization refinements and reverses of the Young and Heinz inequalities, Results Math. 19, 757–768, 2016.
  3. T. Ando, Matrix Young inequality, Oper. Theory Adv. Appl. 75, 33–38, 1995.
  4. D. Choi, Multiple-Term refinements of Young type inequalities, Hindawi, Journal of Mathematics 2016, Article ID 4346712, 1–11.
  5. R. A. Horn and C.R, Johnson, Matrix Analysis, Cambridge Univ. Press, New-York, 1985.
  6. M. A. Ighachane, M. Akkouchi and El Hassan Benabdi, A new generalized refinement of the weighted arithmetic-geometric mean inequality, Mathematical Inequalities and Applications 23 (3), 1079–1085, 2020.
  7. M. A. Ighachane and M. Akkouchi, A new generalized refinement of Yong’s inequality and applications, Journal. Math. Inequalities, Accepted.
  8. M. A. Ighachane and M. Akkouchi, Further generalized refinement of Young’s inequalities for \tau-mesurable operators, Moroccan J. Pure Appl. Anal. 7 (2), 214–226, 2021.
  9. M. A. Ighachane and M. Akkouchi, A new generalization of two refined Young inequalities and applications, Moroccan J. Pure Appl. Anal. 6 (2), 155–167, 2020.
  10. H. Kai, Young type inequalities for matrices, Journal of East China Normal University (Natural Science) 4, 12–17, 2012.
  11. F. Kittaneh and Y. Manasrah, Improved Young and Heinz inequalities for matrices, J. Math. Anal. Appl. 36, 292–269, 2010.
  12. F. Kittaneh, Norm inequalities for fractionl powers of positive operators, Lett. Math. Phys. 27, 279–285, 1993.
  13. L. Nasiri, M. Shakoori and W.Liao, A note of the Young type inequalities, Int. J. Nonlinear Anal. Appl, 8 (1), 261–267, 2017.
  14. J. Pečarić, T. Furuta, T. Mićić and T. Seo, Mond-Pe’ carić method in operator inequalities, Element, Zagreb, 2005.
  15. M. Sababheh and D. Choi, A complete refinement of Young’s inequality, J. Math. Anal. Appl. 440 (1), 379–393, 2016.
  16. C. Yang and Y. Li, Refinements and reverses of Young’s type inequalities, Journal. Math. Inequalities 14, 401–419, 2020.