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Volume 10, Issue 4, Article 95 |
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Inequalities for $J-$Contractions Involving the $ \alpha-$Power Mean
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Authors: |
G. Soares, |
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Keywords:
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$J-$selfadjoint matrix, Furuta inequality, $J-$chaotic order, $lpha-$power mean. |
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Date Received:
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22/06/2009 |
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Date Accepted:
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14/10/2009 |
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Subject Codes: |
47B50, 47A63, 15A45.
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Editors: |
Sever S. Dragomir, |
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Abstract: |
A selfadjoint involutive matrix  endows  with an indefinite inner product ![$[ cdot, cdot]$](images/168_09_JIPAM/img3.gif) given by ![$[x,y]:= langle J x, y rangle$](images/168_09_JIPAM/img4.gif) ,  We present some inequalities of indefinite type involving the  power mean and the chaotic order. These results are in the vein of those obtained by E. Kamei [6, 7].
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