mean with respect to a function

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  1. Michael Penn
  2. math
  3. mathematics
  4. number theory
  5. abstract algebra
  6. calculus
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Комментарии
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this AM-GM inequality result is nice in the sense that for the log mean, c in (a, b) actually resides in (sqrt(ab), 0.5 * (a + b)), which is a tighter interval, and hence we get tighter bounds.

Usually bounds are loosened for substantiating proofs, but this result does the exact opposite

broomstick
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I hate when YouTube app in my iPhone suddenly stops in middle of a short and doesn’t buffer further even if I am connected to 100 Mbps of internet.😡

mayankmrinal
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Cool concept. Any practical application? Are the traditional mean (arithmetic, geometric mean) particular cases of this definition? So basically are there any function f and g so that the arithmetic mean is the mean with respect to f, and the geometric mean is the mean with respect to g?

adumont
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Nice concept, but is it not easy to have several means in this case? There could be several points where the derivative is equal to the overall rate of change? Usually means are uniquely defined.

aaasm