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 August 26th, 2014, 12:04 PM #1 Member   Joined: Mar 2013 Posts: 71 Thanks: 4 prove that $gof:I \rightarrow \mathbb R$ is also convex Good afternoon! I'm in trouble to prove the folowing problem: "Let $f:I \rightarrow \mathbb R$ and $g:J \rightarrow \mathbb R$ be convex mappings with $f(I) \subset J$, $g$ monotonic, non decreasing. a) prove that $gof:I \rightarrow \mathbb R$ is also convex. b) give another demonstration of (a), using the fact that $f$ and $g$ are twice differentiable. c) give an exemple to show that if $g$ is not non decreasing, then the result doesn't necessarily hold My solution: a) Since $f$ is convex, then for $x,y \in I$, $0 \le t \le 1, 0 \le r \le 1, t+r=1, f(tx+ry)\le tf(x)+rf(y)$. Now I use the fact that $g$ is monotonic non-decreasing, i.e, $x  Tags$gofi, convex, mathbb, prove, rightarrow Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post walter r Abstract Algebra 2 August 8th, 2014 04:30 PM Singularity Abstract Algebra 5 January 23rd, 2013 10:53 PM Vasily Applied Math 1 June 30th, 2012 02:57 PM galois Algebra 0 November 4th, 2010 03:39 AM frederico Real Analysis 0 April 6th, 2009 11:31 AM

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