Positive Semidefinite Matrices, Exponential Convexity for Majorization, and Related Cauchy Means
<p/> <p>We prove positive semidefiniteness 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 intr...
Main Authors: | , , |
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Format: | Article |
Language: | English |
Published: |
SpringerOpen
2010-01-01
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Series: | Journal of Inequalities and Applications |
Online Access: | http://www.journalofinequalitiesandapplications.com/content/2010/728251 |
Summary: | <p/> <p>We prove positive semidefiniteness 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 introduce new Cauchy means and show that these means are monotone.</p> |
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ISSN: | 1025-5834 1029-242X |