在数学中，函数的不动点或定点是指被这个函数映射到其自身一个点。例如，定义在实数上的函数，

则是函数的一个不动点，因为。

也不是每一个函数都具有不动点。例如定义在实数上的函数就没有不动点。因为对于任意的实数，永远不会等于。用画图的话来说，不动点意味着点在直线上，或者换句话说，函数的图像与那根直线有共点。上例的情况是，这个函数的图像与那根直线是一对平行线。

在函数的有限次迭代之后回到相同值的点叫做周期点；不动点是周期等于 1 的周期点。

In mathematics, a fixed point (sometimes shortened to fixpoint, also known as an invariant point) of a function is an element of the function's domain that is mapped to itself by the function. That is to say, c is a fixed point of the function f(x) if and only if f(c) = c. This means f(f(...f(c)...)) = f(c) = c, an important terminating consideration when recursively computing f. A set of fixed points is sometimes called a fixed set.