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Function with 2016 variables

Source: Azerbaijan NMO 2016. Senior P5

July 27, 2023
functionalgebra

Problem Statement

Let R\mathbb R be the set of real numbers. Determine all functions f:R→Rf:\mathbb R\to\mathbb R that satisfy the equation ∑i=12015f(xi+xi+1)+f(∑i=12016xi)≤∑i=12016f(2xi)\sum_{i=1}^{2015} f(x_i + x_{i+1}) + f\left( \sum_{i=1}^{2016} x_i \right) \le \sum_{i=1}^{2016} f(2x_i) for all real numbers x1,x2,...,x2016.x_1, x_2, ... , x_{2016}.
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