2018-16 A convex function

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

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2018-16 A convex function, 4.6 out of 5 based on 9 ratings