Inequality for convex function

Reference no: EM13117698

Let a < b be real numbers and f: [a,b] -> R a convex function (equivalently a concave upward function). Define

F(s,t) = f (s) + f(t) - 2f((s+t)/2)

Prove that F(s,t) ≤ F(a,b) for every s,t ∈[a,b].

Reference no: EM13117698

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