Positive semi-definite matrices, exponential convexity for multiplicative majorization and related means of Cauchy's type-Reference-Cited by-同舟云学术

Positive semi-definite matrices, exponential convexity for multiplicative majorization and related means of Cauchy's type

Published:2010-02-01 Issue:1 Volume:39 Page:50-68
ISSN:2501-059X
Container-title:Journal of Numerical Analysis and Approximation Theory
language:
Short-container-title:J. Numer. Anal. Approx. Theory

Author:

Latif Naveed,Pečarić Josip

Abstract

In this paper, we obtain new results concerning the generalizations of additive and multiplicative majorizations by means of exponential convexity. We prove positive semi-definiteness of matrices generated by differences deduced from majorization type results which implies exponential convexity and \(\log\)-convexity of these differences and also obtain Lyapunov's and Dresher's inequalities for these differences. We give some applications of additive and multiplicative majorizations. In addition, we introduce new means of Cauchy's type and establish their monotonicity.

Publisher

Academia Romana Filiala Cluj

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis,Mathematics (miscellaneous)

Link

https://ictp.acad.ro/jnaat/journal/article/download/2010-vol39-no1-art5/Latif-Pecaric-pdf

Reference11 articles.

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