In mathematics, the Fekete–Szegő inequality is an inequality for the coefficients of univalent

analytic functions In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions. Functions of each type are infinitely differentiable, but complex ...

found by , 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 :

f(z)=z+a_2z^2+a_3z^3+\cdots

is a univalent analytic function on the unit disk and

0\leq \lambda < 1

, then :

, a_3-\lambda a_2^2, \leq 1+2\exp(-2\lambda /(1-\lambda)).

References

* Inequalities (mathematics) {{mathanalysis-stub