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Volume 3, Issue 5, Article 82 |
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Improved $GA$- Convexity Inequalities
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Authors: |
Razvan A. Satnoianu, |
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Keywords:
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Convex functions, $GA$-convexity, Symmetric functions, IMO competition. |
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Date Received:
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10/07/02 |
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Date Accepted:
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05/08/02 |
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Subject Codes: |
26D15,26D10,39B62,52A40.
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Editors: |
Constantin P. Niculescu, |
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Abstract: |
We consider a class of algebraic inequalities for functions of
n variables depending on parameters that generalise the case of
GA-convex functions. The functions in this class are GA-convex only in a subdomain of
definition yet the inequality for GA-convexity still holds on the whole
domain if suitable conditions are satisfied by the parameters. The method is
elementary and allows us to give further extensions to a large class of
functions.
As an application we show the validity of an n-dimensional generalization of
a conjectured inequality related to a problem given at the 42nd IMO held
in Washington DC (USA) in 2001.
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