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Let $E_n(R)$ be a sequence of function that converge to $E(R)$, When we can said that $\dot{E}_n(R)$ converge to $\dot{E}(R)$.

I can assume:

  1. uniform converge of $E_n$ to $E$.
  2. $E(R)$ convex.
  3. Continuety of $\ddot{E}$
  4. Monotonicity of $E_n$ os that the example of $\frac{1}{n}\sin(nx)$ does not work.

I need a positive result so if other condition needed for converge, its OK to point them.

Thanks !

nir
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  • Possible duplicate: http://math.stackexchange.com/questions/265930/limit-of-derivatives-of-convex-functions – Siméon Sep 19 '14 at 11:52
  • It is similar. they assumed convexity of the sequence. I don't want to assume that. – nir Sep 19 '14 at 20:21

1 Answers1

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My smart book says:

  1. Uniform convergence of series $\dot{E_n},\,\,x\in \langle a, b\rangle$
  2. Convergence of series $E_n$ at least one point $\in \langle a, b\rangle $(from points 1 and 2 $\Rightarrow$ series $E_n$ convergent uniformly in the interval $\langle a, b\rangle $)

No additional conditions.

georg
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