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  Volume 3, Issue 5, Article 82
 
Improved $GA$- Convexity Inequalities

    Authors: Razvan A. Satnoianu,  
    Keywords: Convex functions, $GA$-convexity, Symmetric functions, IMO competition.  
    Date Received: 10/07/02  
    Date Accepted: 05/08/02  
    Subject Codes:

26D15,26D10,39B62,52A40.

 
    Editors: Constantin P. Niculescu,  
 
    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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