Full Idea
If a function f maps the argument a back to a itself, so that f(a) = a, then a is said to be a 'fixed point' for f.
Gist of Idea
An argument is a 'fixed point' for a function if it is mapped back to itself
Source
Peter Smith (Intro to Gödel's Theorems [2007], 20.5)
Book Reference
Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.174