Nonlinear functional analysis
# Nonlinear functional analysis

Nonlinear functional analysis is a branch of mathematical analysis that deals with nonlinear mappings.

## Topics

Its subject matter $includes:^{:1–2}$

* generalizations of calculus to Banach spaces
* implicit function theorems
* fixed-point theorems (Brouwer fixed point theorem, Fixed point theorems in infinite-dimensional spaces, topological degree theory, Jordan separation theorem, Lefschetz fixed-point theorem)
* Morse theory and Lusternik–Schnirelmann category theory
* methods of complex function theory
