A fixed point, sometimes called a fixpoint or invariant point, is a value that a given transformation leaves unchanged. For a function, a fixed point is an element that the function maps to itself, and the set of all fixed points of a transformation is itself an invariant set. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
Origin YearMarks the Brouwer fixed-point theorem (1911), the first landmark general fixed-point result in mathematics; the everyday notion of a value left unchanged by a transformation is older and not independently datable as a single origin. Connections
Associated With
The theorem guarantees a fixed point exists for any continuous self-map of a nonempty compact convex set, so its conclusion is the fixed point concept applied.
Additional Source Fixed Point (Mathematics) (Wikipedia)Lead section
Sources
1. Fixed Point (Mathematics) (Wikipedia)
Wikimedia FoundationLead section
a fixed point (sometimes shortened to fixpoint), also known as an invariant point, is a value that does not change under a given transformation
Fixed-point theorems section
The Brouwer fixed-point theorem (1911) says that any continuous function from the closed unit ball in n-dimensional Euclidean space to itself must have a fixed point, but it does not describe how to find the fixed point.
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