MathDB
f(x+y)>= f(x)+ f(y) if f(x)/x increasing (I Soros Olympiad 1994-95 R1 11.5)

Source:

August 1, 2021
functioninequalitiesalgebra

Problem Statement

Function f(x)f(x). which is defined on the set of non-negative real numbers, acquires real values. It is known that f(0)≤0f(0)\le 0 and the function f(x)/xf(x)/x is increasing for x>0x>0. Prove that for arbitrary x≥0x\ge 0 and y≥0y\ge 0, holds the inequality f(x+y)≥f(x)+f(y)f(x+y)\ge f(x)+ f(y) .
Back to ProblemsView on AoPS