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 Post subject: interesting polynomial type inequalityPosted: Tue, 24 Jul 2012 08:04:01 UTC
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Joined: Sun, 23 Mar 2008 10:55:47 UTC
Posts: 27
If is even integer and prove that

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 Post subject: Re: interesting polynomial type inequalityPosted: Wed, 25 Jul 2012 08:58:05 UTC
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Joined: Mon, 29 Dec 2008 17:49:32 UTC
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mathemagics wrote:
If is even integer and prove that

Hint:
Spoiler:
The desired inequality is equivalent to

which follows from the proof of

Edit: correction.

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 Post subject: Re: interesting polynomial type inequalityPosted: Thu, 26 Jul 2012 14:49:51 UTC
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Joined: Sun, 23 Mar 2008 10:55:47 UTC
Posts: 27
Could you please give more details?

I can't see how you get the first inequality by the second one and how you prove it (the second one).

For example the C-S inequality gives that:

and if we accept the second inequality then I don't think that this helps to get the first one because (look the opposite boxed inequality below):

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 Post subject: Re: interesting polynomial type inequalityPosted: Thu, 26 Jul 2012 21:55:41 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
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This is a proposed problem, he doesn't have to post more. If you need this for homework or something, it should be on another board.

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 Post subject: Re: interesting polynomial type inequalityPosted: Fri, 27 Jul 2012 05:18:04 UTC
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Oops, I forgot the words "the proof of" after "follows from", now corrected.

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 Post subject: Re: interesting polynomial type inequalityPosted: Fri, 27 Jul 2012 05:22:42 UTC
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