MathDB
IMO Shortlist 2009 - Problem A5

Source:

July 5, 2010
functioninequalitiesalgebraFunctional inequalityIMO Shortlist

Problem Statement

Let ff be any function that maps the set of real numbers into the set of real numbers. Prove that there exist real numbers xx and yy such that f(xāˆ’f(y))>yf(x)+xf\left(x-f(y)\right)>yf(x)+x
Proposed by Igor Voronovich, Belarus
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