Nonlinear functional analysis
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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