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I would like to solve the following inequality:

$\frac{(\rho +\tau -1) \left(n g'(n) \left((g(n)-c) F'(g(n))+F(g(n))-1\right)+(c-g(n)) (F(g(n))-1)\right)}{n^2}>0$

Under some assumptions (listed below). I am using the Reduce command:

Reduce[(-1 + \[Rho] + \[Tau]) ((-1 + F[g[n]]) (c - g[n]) + 
      n (-1 + F[
          g[n]] + (-c + g[n]) Derivative[1][F][g[n]]) Derivative[1][
        g][n]) > 0 && ForAll[n, Derivative[1][g][n] < 0] && 
  ForAll[n, Derivative[1][F][g[n]] > 0] && ForAll[n, g[n] > c > 0] && 
  ForAll[n, 0 < F[g[n]] < 1] && n > 0 && 0 < \[Rho] < 1 && 
  0 < \[Tau] < 1 && n > 0 && 0 < \[Rho] + \[Tau] < 1]

but the output says: "This system cannot be solved with the methods available to Reduce".

Would you have any suggestions on how to do this?

Thanks in advance

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  • $\begingroup$ A portion of your code appears to be missing $\endgroup$
    – Bob Hanlon
    Jan 29, 2023 at 14:52
  • $\begingroup$ @BobHanlon Thanks. Now should it work? $\endgroup$
    – MaB21
    Jan 29, 2023 at 14:53

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