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determine all functions...

Source: Romanian District Olympiad 2015, Grade XII, Problem 3

September 26, 2018

functioncontinuitymonotone functionsFind all functionsreal analysis

Problem Statement

Find all continuous and nondecreasing functions

f:[0,\infty)\longrightarrow\mathbb{R}

that satisfy the inequality: \int_0^{x+y} f(t) dt\le \int_0^x f(t) dt +\int_0^y f(t) dt, \forall x,y\in [0,\infty) .