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Is that true that the limiting function which is a function series of convex functions is also convex?

I'm not sure what is the exact name of this "limiting function" in English, after the German terminology this is "Grenzfunktion" .

I mean this " A sequence of functions $ (f_{n}) $converges uniformly to a limiting function $ f$ on a set $ E $"

Is this maybe the answer to my question?

Proving that a limit of a convex functions is convex

I appreciate any kind of help.

Herrpeter
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  • As far as I know, the English word is "limit function" or simply "limit" (if there is no possibility of misunderstanding). – ComplexF Apr 02 '18 at 17:08
  • In English the phrase " $f$ is the uniform limit of a sequence $(f_n)n$ of functions" is common. ...And "function sequence" should not be used, due to the undefinability of English grammar. ... In English a "series" usually means something like $\sum{n=1}^{\infty}A_n.$ – DanielWainfleet Apr 03 '18 at 03:10
  • Your proposed link is exactly what you need. – DanielWainfleet Apr 03 '18 at 03:12

1 Answers1

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Finite sums of convex functions are convex and pointwise limit of convex functions is convex so the sum of a pointwise convergent series of convex functions is also convex.

Kavi Rama Murthy
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