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Generalizations of a Matrix Inequality

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DOI: 10.4236/am.2014.53034    3,993 Downloads   6,122 Views  

ABSTRACT

In this paper, some new generalizations of the matrix form of the Brunn-Minkowski inequality are presented.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

L. Zhao, J. Yuan and Y. Cai, "Generalizations of a Matrix Inequality," Applied Mathematics, Vol. 5 No. 3, 2014, pp. 337-341. doi: 10.4236/am.2014.53034.

References

[1] I. J. Bakelman, “Convex Analysis and Nonlinear Geometric Elliptic Equations,” Springer, Berlin, 1994.
http://dx.doi.org/10.1007/978-3-642-69881-1
[2] C. Borell, “The Brunn-Minkowski Inequality in Gauss Space,” Inventiones Mathematicae, Vol. 30, No. 2, 1975, pp. 202-216.
http://dx.doi.org/10.1007/BF01425510
[3] C. Borell, “Capacitary Inequality of the Brunn-Minkowski Inequality Type,” Mathematische Annalen, Vol. 263, No. 2, 1993, pp. 179-184. http://dx.doi.org/10.1007/BF01456879
[4] K. Fan, “Some Inequality Concerning Positive-Denite Hermitian Matrices,” Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 51, No. 3, 1958, pp. 414-421.
http://dx.doi.org/10.1017/S0305004100030413
[5] R. J. Gardner and P. Gronchi, “A Brunn-Minkowski Inequality for the Integer Lattice,” Transactions of the American Mathematical Society, Vol. 353, No. 10, 2001, pp. 3995-4024.
http://dx.doi.org/10.1090/S0002-9947-01-02763-5
[6] R. J. Gardner, “The Brunn-Minkowski Inequality,” Bulletin of the American Mathematical Society, Vol. 39, No. 3, 2002, pp. 355-405. http://dx.doi.org/10.1090/S0273-0979-02-00941-2
[7] G. S. Leng, “The Brunn-Minkowski Inequality for Volume Differences,” Advances in Applied Mathematics, Vol. 32, No. 3, 2004, pp. 615-624. http://dx.doi.org/10.1016/S0196-8858(03)00095-2
[8] R. Osserman, “The Brunn-Minkowski Inequality for Multiplictities,” Inventiones Mathematicae, Vol. 125, No. 3, 1996, pp. 405-411. http://dx.doi.org/10.1007/s002220050081
[9] E. V. Haynesworth, “Note on Bounds for Certain Determinants,” Duke Mathematical Journal, Vol. 24, No. 3, 1957, pp. 313320. http://dx.doi.org/10.1215/S0012-7094-57-02437-7
[10] E. V. Haynesworth, “Bounds for Determinants with Positive Diagonals,” Transactions of the American Mathematical Society, Vol. 96, No. 3, 1960, pp. 395-413. http://dx.doi.org/10.1090/S0002-9947-1960-0120242-1
[11] M. Marcus and H. Minc, “A Survey of Matrix Theory and Inequalities,” Allyn and Bacon, Boston, 1964.
[12] R. Bellman, “Introduction to Matrix Analysis,” McGraw-Hill, New York, 1960.
[13] R. Horn and C. R. Johnson, “Matrix Analysis,” Cambridge University Press, New York, 1985.
http://dx.doi.org/10.1017/CBO9780511810817
[14] E. F. Beckenbach and R. Bellman, “Inequalities,” Springer, Berlin, 1961.
http://dx.doi.org/10.1007/978-3-642-64971-4

  
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