Univalent function: Difference between revisions

Revision as of 04:45, 9 January 2014

Revision as of 04:46, 9 January 2014

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:<math>f: G \to \Omega</math>

is a univalent function such that <math>f(G) = \Omega</math> (that is, <math>f</math> is [[ontoSurjective_function|surjective]]), then the derivative of <math>f</math> is never zero, <math>f</math> is [[invertible]], and its inverse <math>f^{-1}</math> is also holomorphic. More, one has by the [[chain rule]]

:<math>(f^{-1})'(f(z)) = \frac{1}{f'(z)}</math>