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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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