MathDB

Asymmetric functional inequality from the Netherworld

Source: 2023 Dutch BxMO TST, Problem 2

March 12, 2024

Functional EquationsFunctional inequalityalgebra

Problem Statement

Find all functions

f : \mathbb R \to \mathbb R

for which

f(a - b) f(c - d) + f(a - d) f(b - c) \leq (a - c) f(b - d),

for all real numbers

a, b, c

and

d

. Note that there is only one occurrence of

f

on the right hand side!