Explore: Fixed Points

Fixed point may refer to: Fixed point (mathematics), a value that does not change under a given transformation Fixed-point arithmetic, a manner of doing

the variable that occurs repeatedly after intervals of a fixed length. These periodic points play a role in the theories of Fatou and Julia sets. Let

{\displaystyle f} has one or more fixed points, then f i x   f {\displaystyle \mathrm {fix} \ f} is one of these fixed points, i.e., f i x   f   = f   ( f

then the existence of modal fixed points follows from the diagonal lemma. In addition to the existence of modal fixed points, we assume the following rules

and uniqueness of fixed points of certain self-maps of metric spaces and provides a constructive method to find those fixed points. It can be understood

transformations are those where the fixed points coincide. Either or both of these fixed points may be the point at infinity. The fixed points of the transformation

Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function f

Specifically, for functions, a fixed point is an element that is mapped to itself by the function. Any set of fixed points of a transformation is also an

existence of two fixed points Ryll-Nardzewski fixed-point theorem Schauder fixed-point theorem Topological degree theory Tychonoff fixed-point theorem Trace

fixed point of the real function f(x) = x2 is x = 0 (since the only other fixed point is 1 and 0 < 1). In contrast, f(x) = x + 1 has no fixed points at