In mathematics, the Fekete–Szegő inequality is an inequality for the coefficients of univalent analytic functions found by Fekete and Szegő ( 1933), related to the Bieberbach conjecture. Finding similar estimates for other classes of functions is called the Fekete–Szegő problem.

The Fekete–Szegő inequality states that if

${\displaystyle f(z)=z+a_{2}z^{2}+a_{3}z^{3}+\cdots }$

is a univalent analytic function on the unit disk and ${\displaystyle 0\leq \lambda <1}$, then

${\displaystyle |a_{3}-\lambda a_{2}^{2}|\leq 1+2\exp(-2\lambda /(1-\lambda )).}$

References

• Fekete, M.; Szegő, G. (1933), "Eine Bemerkung über ungerade schlichte Funktionen", Journal of the London Mathematical Society, 8 (2): 85–89, doi: 10.1112/jlms/s1-8.2.85

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