MathDB
Locally bounded function with strange integral inequality

Source: Alibaba Global Math Competition 2021, Problem 6

July 4, 2021
functionMeasure theoryInequalitycalculusintegrationcollege contestsinequalities

Problem Statement

Let M(t)M(t) be measurable and locally bounded function, that is, M(t) \le C_{a,b},   \forall 0 \le a \le t \le b<\infty with some constant Ca,bC_{a,b}, from [0,∞)[0,\infty) to [0,∞)[0,\infty) such that M(t) \le 1+\int_0^t M(t-s)(1+t)^{-1}s^{-1/2} ds,   \forall t \ge 0. Show that M(t) \le 10+2\sqrt{5},   \forall t \ge 0.
Back to ProblemsView on AoPS