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Is there a way of proving that a function has a particular number of fixed points.

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0

1

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From my understanding, a function is said to have a fixed point if $f(x) = x$.

Is there a way for finding how many fixed points a function has?

functions fixed-point-theorems fixedpoints

share|cite|improve this question

edited Mar 9 at 17:37

Daniele Tampieri

2,3972922

asked Mar 9 at 17:33

therewillbecodetherewillbecode

101

New contributor

therewillbecode is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

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  In this level of generality? No. Given a specific function, maybe! Do you have one that you're interested in?
  $endgroup$
  – Billy
  Mar 9 at 17:35
  

  
  
  
  


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  $begingroup$
  Brouwer’s Fixed Point Theorem is a result of the existence of a fixed point. So is the Banach Fixed-Point Theorem. But there are some assumptions that go along with them.
  $endgroup$
  – Ekesh Kumar
  Mar 9 at 17:55
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You are asking how one can find all zeros of function $phi$ defined by $phi(x):=f(x)-x$...
  $endgroup$
  – Jean Marie
  Mar 9 at 18:24
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Basically you need to solve the equation f(x)-x=0. In some cases it is straight forward in some others in more complicated. For example: for x+2 you solve (x+2)-x=0 which tells you there is no such. On the other end x^2 has the solutions x^2-x+0 result x=0 and x=1 as fixed points (not more!).
  $endgroup$
  – Moti
  Mar 9 at 18:26
  

  
  
  
  

add a comment | 

0

1

$begingroup$

From my understanding, a function is said to have a fixed point if $f(x) = x$.

Is there a way for finding how many fixed points a function has?

functions fixed-point-theorems fixedpoints

share|cite|improve this question

edited Mar 9 at 17:37

Daniele Tampieri

2,3972922

asked Mar 9 at 17:33

therewillbecodetherewillbecode

101

New contributor

therewillbecode is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  In this level of generality? No. Given a specific function, maybe! Do you have one that you're interested in?
  $endgroup$
  – Billy
  Mar 9 at 17:35
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Brouwer’s Fixed Point Theorem is a result of the existence of a fixed point. So is the Banach Fixed-Point Theorem. But there are some assumptions that go along with them.
  $endgroup$
  – Ekesh Kumar
  Mar 9 at 17:55
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You are asking how one can find all zeros of function $phi$ defined by $phi(x):=f(x)-x$...
  $endgroup$
  – Jean Marie
  Mar 9 at 18:24
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Basically you need to solve the equation f(x)-x=0. In some cases it is straight forward in some others in more complicated. For example: for x+2 you solve (x+2)-x=0 which tells you there is no such. On the other end x^2 has the solutions x^2-x+0 result x=0 and x=1 as fixed points (not more!).
  $endgroup$
  – Moti
  Mar 9 at 18:26
  

  
  
  
  

add a comment | 

$begingroup$

From my understanding, a function is said to have a fixed point if $f(x) = x$.

Is there a way for finding how many fixed points a function has?

functions fixed-point-theorems fixedpoints

share|cite|improve this question

edited Mar 9 at 17:37

Daniele Tampieri

2,3972922

asked Mar 9 at 17:33

therewillbecodetherewillbecode

101

New contributor

therewillbecode is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|cite|improve this question

edited Mar 9 at 17:37

Daniele Tampieri

2,3972922

asked Mar 9 at 17:33

therewillbecodetherewillbecode

101

New contributor

therewillbecode is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|cite|improve this question

edited Mar 9 at 17:37

Daniele Tampieri

2,3972922

asked Mar 9 at 17:33

therewillbecodetherewillbecode

101

New contributor

therewillbecode is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

edited Mar 9 at 17:37

Daniele Tampieri

2,3972922

edited Mar 9 at 17:37

Daniele Tampieri

2,3972922

asked Mar 9 at 17:33

therewillbecodetherewillbecode

101

New contributor

therewillbecode is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked Mar 9 at 17:33

therewillbecodetherewillbecode

101