IJPAM: Volume 80, No. 3 (2012)

ON THE ARITHMETIC COMPENSATION METHOD

Vasile Cirtoaje
Department of Automatic Control and Computers
University of Ploiesti
Ploiesti, 100680, ROMANIA


Abstract. The arithmetic compensation method is a power tool which can be used to prove many symmetric inequalities of the form $F(x_1,x_2,\cdots,x_n)\ge 0$, where $x_1,x_2,\cdots,x_n$ are nonnegative real variables satisfying $x_1+x_2+\cdots+x_n=s$, $s>0$. Notice that the AC-method can be applied especially to those inequalities where equality holds when some variables are equal and the others are zero. Several applications are given to show the feasibility and effectiveness of the AC-method.

Received: May 31, 2012

AMS Subject Classification: 26D05

Key Words and Phrases: arithmetic compensation, contradiction method, global minimum

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 80
Issue: 3