MathDB
China Mathematical Olympiad 1989 problem6

Source: China Mathematical Olympiad 1989 problem6

October 29, 2013
functioninequalitiesalgebra unsolvedalgebra

Problem Statement

Find all functions f:(1,+∞)→(1,+∞)f:(1,+\infty) \rightarrow (1,+\infty) that satisfy the following condition: for arbitrary x,y>1x,y>1 and u,v>0u,v>0, inequality f(xuyv)≤f(x)14uf(y)14vf(x^uy^v)\le f(x)^{\dfrac{1}{4u}}f(y)^{\dfrac{1}{4v}} holds.
Back to ProblemsView on AoPS