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Beautiful functional equation-inequality, ZIMO-09

Source: International Zhautykov Olympiad 2009, day 1, problem 2

January 17, 2009

inequalitiesfunctionalgebra proposedalgebra

Problem Statement

Find all real

a

, such that there exist a function

f: \mathbb{R}\rightarrow\mathbb{R}

satisfying the following inequality: x\plus{}af(y)\leq y\plus{}f(f(x)) for all

x,y\in\mathbb{R}