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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

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Difference between harmonic mean of arithmetic means and arithmetic mean of harmonic means

Let $S=\{(x_i, y_i)\}_{i=1...n} \in [0,1]^{2n}$ bet a tuple of ordered pairs, and let $A, H$ denote the arithmetic and harmonic mean. Then $$ \sup_S (H(\underset{i}{A}(x_i),\underset{i}{A}(y_i)) - \un …
Sebastian Burst's user avatar