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$f(x) \geq A x$

Source: 41-st Vietnamese Mathematical Olympiad 2003

March 10, 2007
functioninductionlimitalgebra proposedalgebra

Problem Statement

Let F\mathcal{F} be the set of all functions f:(0,∞)→(0,∞)f : (0,\infty)\to (0,\infty) such that f(3x)≥f(f(2x))+xf(3x) \geq f( f(2x) )+x for all xx. Find the largest AA such that f(x)≥Axf(x) \geq A x for all f∈Ff\in\mathcal{F} and all xx.
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