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In mathematics, the '''Fekete–Szegő inequality''' is an inequality for the coefficients of [[univalent function|univalent]] [[analytic functions]] found by {{harvs|txt|last=Fekete|authorlink=Michael Fekete|last2=Szegő|author2-link=Gábor Szegő|year=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
 
:<math>f(z)=z+a_2z^2+a_3z^3+\cdots</math>
 
is a univalent analytic function on the unit disk and 0&nbsp;≤&nbsp;λ&nbsp;<&nbsp;1, then
 
:<math>|a_3-\lambda a_2^2|\leq 1+2\exp(-2\lambda /(1-\lambda)).</math>
 
==References==
*{{Citation | last1=Fekete | first1=M. | author1-link=Michael Fekete | last2=Szegő | first2=G. | author2-link=Gábor Szegő | title= Eine Bemerkung über ungerade schlichte Funktionen | doi=10.1112/jlms/s1-8.2.85  | year=1933 | volume=8 | pages=85–89}}
 
{{DEFAULTSORT:Fekete-Szego inequality}}
[[Category:Inequalities]]

Revision as of 09:07, 28 September 2013

In mathematics, the Fekete–Szegő inequality is an inequality for the coefficients of univalent analytic functions found by Template:Harvs, 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+a2z2+a3z3+

is a univalent analytic function on the unit disk and 0 ≤ λ < 1, then

|a3λa22|1+2exp(2λ/(1λ)).

References

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