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 In complex analysis, de Branges's theorem, or the Bieberbach conjecture, is a theorem that gives a necessary condition on a holomorphic function in order for it to map the open unit disk of the complex plane injectively to the complex plane. It was ...

. 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

* {{DEFAULTSORT:Fekete-Szego inequality Inequalities