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

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?

• In this level of generality? No. Given a specific function, maybe! Do you have one that you're interested in? – Billy Mar 9 at 17:35
• 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. – Ekesh Kumar Mar 9 at 17:55
• You are asking how one can find all zeros of function $\phi$ defined by $\phi(x):=f(x)-x$... – Jean Marie Mar 9 at 18:24
• 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!). – Moti Mar 9 at 18:26