MathDB
Functional Inequality (is back)

Source: 2021 MEMO T-1

September 5, 2021
functional equationFunctional inequalityalgebramemoMEMO 2021

Problem Statement

Determine all functions f:R→Rf: \mathbb{R} \to \mathbb{R} such that the inequality f(x2)−f(y2)≤(f(x)+y)(x−f(y)) f(x^2)-f(y^2) \le (f(x)+y)(x-f(y)) holds for all real numbers xx and yy.
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