Nonlinear functional analysis

Nonlinear functional analysis is a branch of Mathematical Analysis. It deals with nonlinear mappings and its subject matter includes:^[1]: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 Lyusternik–Schnirelmann category theory
• methods of complex function theory

Notes

1. ^ Schwartz, Jacob T. (1969). Non-Linear Functional Analysis. New York: Gordon & Breach Science Pub. ISBN 9780677015057. 

See also

• Functional analysis

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