309
Views
28
CrossRef citations to date
0
Altmetric
Articles

Young-type inequalities and their matrix analogues

, &
Pages 622-635 | Received 26 Nov 2013, Accepted 20 Jan 2014, Published online: 13 Jun 2014

References

  • Young WH. On classes of summable functions and their Fourier series. Proc. Royal Soc. London, Ser. A. 1912;87:225–229.
  • Bullen PS, Mitrinović DS, Vasić PM. Means and their inequalities. Dordrecht: Reidel; 1988.
  • Kittaneh F, Manasrah Y. Improved Young and Heinz inequalities for matrices. J. Math. Anal. Appl. 2010;361:262–269.
  • Kittaneh F, Manasrah Y. Reverse Young and Heinz inequalities for matrices. Linear Multilinear Algebra. 2011;59:1031–1037.
  • Bobylyov NA, Krasnosel’skiy MA. Extremum analysis (degenerate cases). [Preprint], Institute of Control. Moscow; 1981 (in Russian).
  • Hirzallah O, Kittaneh F. Matrix Young inequalities for the Hilbert-Schmidt norm. Linear Algebra Appl. 2000;308:77–84.
  • Feng Y. Refinements of Young’s inequalities for matrices. Far East J. Math. Sci. (FJMS). 2012;63:45–55.
  • Furuichi S, Minculete N. Alternative reverse inequalities for Young’s inequality. J. Math. Inequalities. 2011;5:595–600.
  • KuboF, AndoT. Means of positive linear operators. Math. Ann. 1979;246:205–224.
  • Merris R, Pierce S. Monotonicity of positive semidefinite Hermitian matrices. Proc. Am. Math. Soc. 1972;31:437–440.
  • Horn RA, Johnson CR. Matrix analysis. 2nd ed. New York: Cambridge University Press; 2013.
  • Bhatia R. Positive definite matrices. Princeton (NJ): Princeton University Press; 2007.
  • Beckenbach EF, Bellman R. Inequalities. Berlin: Springer; 1983.
  • Horn RA, Johnson CR. Topics in matrix analysis. New York: Cambridge University Press; 1991.
  • Kosaki H. Arithmetic-geometric mean and related inequalities for operators. J. Funct. Anal. 1998;156:429–451.
  • Bhatia R, Parthasarathy KR. Positive definite functions and operator inequalities. Bull. London Math. Soc. 2000;32:214–228.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.