- #36

julian

Gold Member

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The only reason I considered ##\Gamma_n (x)##'s was to prove for finite ##n## that these functions are convex, which would then imply that the limit function ##\lim_{n \rightarrow \infty} \Gamma_n (x)## is convex. I was proving that the limit function stated in the problem satisfies the properties stated in the problem.Well, I tried to provide hints in my previous post. I would be happy if you used less ##G's## and ##\Gamma 's## in your prove. This only creates confusion.

I then wanted to prove that it is is the only function that satisfies the properties (uniqueness proof part) and so I necessarily had to introduce an arbitrary function ##G (x)## that also satisfies the properties stated in the problem.

(I made a few edits to my partial solution to make it a bit clearer and correct some typos)