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Volume 8, Issue 2, Article 51 |
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$S$-Geometric Convexity of a Function Involving Maclaurin's Elementary Symmetric Mean
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Authors: |
Xiao-Ming Zhang, |
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Keywords:
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Geometrically convex function, $S$-geometrically convex function, Inequality, Maclaurin-Inequality, Logarithm majorization. |
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Date Received:
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23/02/07 |
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Date Accepted:
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27/04/07 |
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Subject Codes: |
Primary 26D15.
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Editors: |
Peter S. Bullen, |
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Abstract: |
Let  ,  , the  th elementary symmetric function of  is defined as  , and the function  is defined as  . The paper proves that is a S-geometrically convex function. The result generalizes the well-known Maclaurin-Inequality.
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