Univalent function

In mathematics, in the branch of complex analysis, a holomorphic function on an open subset of the complex plane is called univalent if it is injective.

f(z)=f(w) implies that f is injective.

One can prove that if f:G→Ω

is a univalent function such that f is never zero, (f−1)′(f(z))=1f′(z)

for all f:(−1,1)→(−1,1)

given by (−1,1). Consequently, if we enlarge the domain to an open subset ω is a primitive cube root of unity and 0).

• Biholomorphic mapping – Bijective holomorphic function with a holomorphic inversePages displaying short descriptions of redirect targets
• De Branges's theorem – Statement in complex analysis; formerly the Bieberbach conjecture
• Koebe quarter theorem – Statement in complex analysis
• Riemann mapping theorem – Mathematical theorem
• Nevanlinna's criterion – Characterization of starlike univalent holomorphic functions

• Conway, John B. (1995). "Conformal Equivalence for Simply Connected Regions". Functions of One Complex Variable II. Graduate Texts in Mathematics. Vol. 159. doi:10.1007/978-1-4612-0817-4. ISBN 978-1-4612-6911-3.
• Gong, Sheng (1998). Convex and Starlike Mappings in Several Complex Variables. doi:10.1007/978-94-011-5206-8. ISBN 978-94-010-6191-9.
• This article incorporates material from univalent analytic function on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.