A new generalized refinements of Young’s inequality

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-4468

Keywords:

AM-GM inequality, Young inequality, Determinants, Trace, Norms

Abstract

In this paper, we show a new generalized refinement of Young's inequality. As applications we give some new generalized refinements of Young type inequalities for the traces, determinants, and norms of positive definite matrices.

 

Author Biographies

Mohamed Amine Ighachane, University Cadi Ayyad.

Department of Mathematics. Faculty of Sciences-Semlalia.

Mohamed Akkouchi, University Cadi Ayyad.

Department of Mathematics, Faculty of Sciences-Semlalia.

References

Y. Al- Manasrah and F. Kittaneh, “A generalization of two refined Young inequalities”, Positivity, vol. 19, pp. 757-768, 2015.

Y. Al- Manasrah and F. Kittaneh, “Further Generalization, Refinements, and Reverses of the Young and Heinz Inequalities”, Results in Mathematics, vol. 19, pp. 757-768, 2016.

M. Akkouchi and M. A. Ighachane, “A new proof of a refined Young inequality”, Bulletin of the International Mathematical Virtual Institute, vol. 10, no. 3, pp. 425-428, 2020.

T. Ando, “Matrix Young Inequalities,” in Operator Theory in Function Spaces and Banach Lattices, C. B. Huijsmans, M. A. Kaashoek, W. A. J. Luxemburg, and B. Pagter, Eds. Basel: Birkhäuser, 1995, pp. 33–38.

S. Furuichi, “On refined Young inequalities and reverse inequalities”, Journal of Mathematical Inequalities, vol. 5, pp. 21-30, 2011.

R. A. Horn and C. R. Johnson, Matrix analysis. New York: Cambridge University. Press, 1985.

O. Hirzallah, and F. Kittaneh, “Matrix Young inequalities for the Hilbert-Schmidt norm”, Linear Algebra and its Applications, vol. 308, pp. 77-84, 2000.

T. Kato, “Notes on some inequalities for linear operators”, Mathematische Annalen, vol. 125, pp. 208-212, 1952.

M. A. Ighachane, M. Akkouchi, and El Hassan Benabdi, “A new generalized refinement of the weighted arithmetic-geometric mean inequality”, Mathematical Inequalities and Applications, vol. 23, no. 3, pp. 1079- 1085, 2020.

M. A. Ighachane and M. Akkouchi, “A new generalization of two refined Young inequality”, Moroccan Journal of Pure and Applied Analysis, vol. 6, no. 2, pp. 155-167, 2020.

F. Kittaneh, “Norm inequalities for fractionl powers of positive operators”, Letters in Mathematical Physics, vol. 27, pp. 279-285, 1993.

F. Kittaneh and Y. Al- Manasrah, “Improved Young and Heinz inequalities for matrices”, Journal of Mathematical Analysis and Applications, vol. 361, pp. 292-269, 2010.

J. Zhao and J. Wu, “Operator inequalities involving improved Young and its reverse inequalities”, Journal of Mathematical Analysis and Applications, vol. 421, pp. 1779-1789, 2015.

Published

2021-04-19

How to Cite

[1]
M. A. Ighachane and M. . Akkouchi, “A new generalized refinements of Young’s inequality”, Proyecciones (Antofagasta, On line), vol. 40, no. 5, pp. 1197-1209, Apr. 2021.

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Section

Artículos