
Applied Math Applied Math Forum 
 LinkBack  Thread Tools  Display Modes 
January 31st, 2013, 10:25 AM  #1  
Newbie Joined: Jan 2013 Posts: 4 Thanks: 0  Inequality with minimum function
Dear readers, The variables and constants are more or less based on the definitons in my previous thread: viewtopic.php?f=27&t=37864 There exists a stationary population , so: , where and ( means the amount of people in age group at time . There are age groups, labeled from to ) Let with: , Now I have to show for a arbitrary population that is converges to the stationary distribution . To prove that, let and be 2 general populations. And let (. There are fertile age groups, labeled to )  Show that by using the properties below: with (these also yield for ) and Quote:
 My reasoning: The survival probabilities of are in the numerator and denominator, so they cancel each other out. So the elements in the minimumfunction of and are mostly the same. The only two differences are that has got the fraction and hasn't. On the other hand has got and hasn't. In short, when for all , then . I thought that: , but that doesn't help me either.  Anyone who can lend me a hand?  Fruit Bowl.  

Tags 
function, inequality, minimum 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
minimum value of function  MATHEMATICIAN  Calculus  9  August 31st, 2013 10:33 AM 
minimum of a function  david hilbert  Complex Analysis  3  January 28th, 2013 02:33 AM 
minimum of function with 2 variables  bertusavius  Calculus  1  October 18th, 2012 03:08 AM 
minimum value of function  amateurmathlover  Calculus  4  April 22nd, 2012 12:39 AM 
The minimum of an inequality  LTDH  Elementary Math  1  March 27th, 2011 04:12 AM 