For non-decreasing alphas summing to zero, sum phi(k alpha_k) is nonnegative for any odd increasing convex phi on [0, infinity).
I, East China Normal University Press, 2019, pp
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Inequalities on a Class of Function Sets
For non-decreasing alphas summing to zero, sum phi(k alpha_k) is nonnegative for any odd increasing convex phi on [0, infinity).