一类解析函数的Fekete-Szego不等式

The Fekete-Szego Inequality for A Subclass of Analytic Functions

利用微分从属构造了解析函数类H(α,A,B)={f(z)∈H:(1-α)f(z)/z+αf'(z)<(1+Az)/(1+Bz),z∈U},其中0≤α≤1,-1≤B<A≤1,z∈U.利用施瓦兹函数的Fekete-Szeg ?不等式,得到了该函数类上的a_2及a_3-μa_2~2(μ∈C)的精确估计:a_3-μa_2~2≤(A-B)/(1+2α)max {1|,B+(μ(1+2α)(A-B))/((1+α)~2)},并给出了相应的极值函数,其结果推广了已有的结论.

By making differential subordination, a new function of H（ α,A ,B）={f（z）∈H：（1-α）f（z）/z＋αf＇（z）〈（1＋Az）/（1＋Bz）,z∈U},is introduced, among them,0≤α≤1,-1≤B〈A≤1,z∈U.By using Fekete-Szego inequality of Schwarts function, if f（z）∈H（α,A,B）,μ∈C,then ｜a2｜≤（A-B）/（1＋α） and for all μ∈C εογ following bound is sharp ｜a3-μa2^2｜≤A-B/1＋2αmax{1,｜B＋μ（1＋2α）（A-B）/（1＋α）^2｜}.The extremal function of H（α,A ,B） is given, some existing results are expanded by the conclusion of this article.