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A fixed-point theorem is a result saying that a function $F$ will have at least one fixed point (a point $x$ for which $F(x) = x$), under some conditions on $F$ that can be stated in general terms.

4 votes

Has the Fundamental Theorem of Algebra been proved using just fixed point theory?

Yes you can prove FTA using BFPT. See also recent paper by Daniel Reem relating to Open Mapping Theorem. I often looked at the 1949 note of B.H. Arnold (a professor of mine in bygone times) but miss …
Arne Sjogren's user avatar