title: Nonlinear functional analysis
text: # 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
  