Hey if anyone can help me with these problems, I'd appreciate it..
1) Let F: R->R (reals) be a differentiable map. Show that F is a contraction if |F'| < 1 where F is a function
(I have let F(x) = root(x^2 +1), which isn't a contraction even though the | derivative | is < 1 )
2) For what values of r does the map F: (0,1] -> [0,1], F(x) = r*x*(1-x) have a unique attracting fixed point?
(I know 0<r<4 to have a fixed point, but how do i show this?)
3) How to prove d(x,z) <= (lessthan equalto) d(x,y) + d(y,z) where d(x,y) = |x-y|/ (1 + |x-y| )
(I'm trying to prove it's a metric space In R
If anyone has any info... lemme know
Thanks
1) Let F: R->R (reals) be a differentiable map. Show that F is a contraction if |F'| < 1 where F is a function
(I have let F(x) = root(x^2 +1), which isn't a contraction even though the | derivative | is < 1 )
2) For what values of r does the map F: (0,1] -> [0,1], F(x) = r*x*(1-x) have a unique attracting fixed point?
(I know 0<r<4 to have a fixed point, but how do i show this?)
3) How to prove d(x,z) <= (lessthan equalto) d(x,y) + d(y,z) where d(x,y) = |x-y|/ (1 + |x-y| )
(I'm trying to prove it's a metric space In R
If anyone has any info... lemme know
Thanks