Nonlinear functional analysis



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

Topics
Its subject matter includes:


 * 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