MathDB

f(x) = x if f(x) <= x and f(x + y) <= f(x) + f(y)

Source: 1979 Hungary - Kürschák Competition p2

October 15, 2022

algebrafunctionalFunctional inequalityfunction

Problem Statement

f

is a real-valued function defined on the reals such that

f(x) \le x

and

f(x + y) \le f(x) + f(y)

for all

x, y

. Prove that

f(x) = x

for all

x