A univalent function is a one-to-one function
on its domain .
In modular function theory, a function is called univalent on a subgroup automorphic
under valence 1 (Apostol 1997, p. 84).
The univalent Bloch-Landau constant measures the largest disk guaranteed inside the image of a normalized univalent function,
allowing the disk center to vary. Wikström (2026) obtained the certified bounds
See also Brennan's Conjecture ,
Clunie-Sheil-Small Conjecture ,
Universal
Integral Means Spectrum ,
Valence
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References Apostol, T. M. Modular Functions and Dirichlet Series in Number Theory, 2nd ed. Das, S. "A Counterexample to the Clunie-Sheil-Small
Coefficient-Difference Conjecture via Quasiconformal Maps." 6 Oct 2026. https://arxiv.org/abs/2610.07770 . Wikström,
F. "Bounds for the Univalent Bloch-Landau Constant." 25 Oct 2026. https://arxiv.org/abs/2610.34580 . Referenced
on Wolfram|Alpha Univalent Function
Cite this as:
Weisstein, Eric W. "Univalent Function."
From MathWorld https://mathworld.wolfram.com/UnivalentFunction.html
Subject classifications
if it is automorphic
under 
and has valence 1 (Apostol 1997, p. 84).
and reports AI assistance with the mathematical analysis and verification.
