Improved $GA-$ Convexity Inequalities

Volume 3, Issue 5, 2002

Article 82

IMPROVED GA- CONVEXITY INEQUALITIES

DEPARTMENT OF MATHEMATICS,
CITY UNIVERSITY,
LONDON EC1V 0HB, UK.
E-Mail: r.a.satnoianu@city.ac.uk

Received 10 July, 2002; Accepted 5 August, 2002.
Communicated by: C.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.

Key words:
Convex functions, GA-convexity, Symmetric functions, IMO competition.

2000 Mathematics Subject Classification:
26D15, 26D10, 39B62, 52A40.

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