From: "denis-feldmann" Subject: Re: Little bugger of an inequality Date: Fri, 28 Apr 2000 09:03:31 +0200 Newsgroups: sci.math Summary: [missing] Dave Hughes a �crit dans le message : Pine.GSO.3.95.1000428141440.19225C-100000@tuba00.orchestra.cse.unsw.EDU.AU.. . > Hi there, > > recently doing a real analysis assignment I did one of the questions the > wrong way and came up against this inequality > > for 0 < p < 1 > > 2^(1/p) + 1 < (2^p + 1)^(1/p) > > it's true, and I reckon you can substitute 2 for n >= 1. > > Can anyone think of a proof? (even without the n bit) > > Cheers, Those are called (here at least) Holder's inequality. They are a special case of what is known as convexity inequalities: if f is convex (i.e. f''>0), and 0X^p), the right x,y and k, and you will get your result (and many others) > > Dave Hughes > 3rd year pure maths, UNSW > > > ------------------------------------------------------------------------- > | David Hughes | > | UNSW | > | | > | "Communism is man against man. Socialism is the other way around." | > | | > ------------------------------------------------------------------------- >