Find the minimum \(m\) (if it exists) such that every convex function \(f:[-1,1]\to[-1,1]\) has a constant \(c\) such that \[ \int_{-1}^1 \lvert f(x)-c\rvert \,dx \le m.\]
GD Star Rating
loading...
2018-16 A convex function,
loading...
Find the minimum \(m\) (if it exists) such that every convex function \(f:[-1,1]\to[-1,1]\) has a constant \(c\) such that \[ \int_{-1}^1 \lvert f(x)-c\rvert \,dx \le m.\]