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Volume 10, Issue 1, Article 19 |
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Generalized $\lambda$-Newton Inequalities Revisited
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Authors: |
Jianhong Xu, |
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Keywords:
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Elementary symmetric functions, $lambda$-Newton inequalities, generalized $lambda$-Newton inequalities, arithmetic mean-geometric mean inequality, positive stable matrices, determinant-trace inequality. |
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Date Received:
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23/10/08 |
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Date Accepted:
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10/02/09 |
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Subject Codes: |
05A20, 05E05, 15A15, 15A42, 15A45, 26D05
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Editors: |
Jerry J. Koliha, |
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Abstract: |
We present in this work a new and shorter proof of the generalized  -Newton inequalities for elementary symmetric functions defined on a self-conjugate set which lies essentially in the open right half-plane. We also point out some interesting consequences of the generalized -Newton inequalities. In particular, we establish an improved complex version of the arithmetic mean-geometric mean inequality along with the corresponding determinant-trace inequality for positive stable matrices.
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