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All functions f with f(a^2) - f(b^2) \leq (f(a) + b)(a - f(b))

Source: France JBMO TST 2017, Exam 1, Problem 1

June 25, 2018
functioninequalities

Problem Statement

Determine all functions f:R→Rf: \mathbb R \to \mathbb R which satisfy the inequality f(a2)−f(b2)≤(f(a)+b)(a−f(b)),f(a^2) - f(b^2) \leq \left( f(a) + b\right)\left( a - f(b)\right), for all a,b∈Ra,b \in \mathbb R.
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