Shigeru Furuichi
Abstract
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We give an upper bound for the weighted geometric mean using the weighted arithmetic mean and the weighted harmonic mean. We also give a lower bound for the weighted geometric mean. These inequalities are proven for two invertible positive operators.
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We give an upper bound for the weighted geometric mean using the weighted arithmetic mean and the weighted harmonic mean. We also give a lower bound for the weighted geometric mean. These inequalities are proven for two invertible positive operators.
Key concepts: Harmonic mean, Geometric mean, Mathematics, Weighted geometric mean, Weighted arithmetic mean, Invertible matrix, Operator (biology), Upper and lower bounds