某类积分算子解析函数的性质

Some Properties for Certain Integral Operator on Analytic Functions

设A是单位圆盘U={z:z<1,z∈C}内的单叶解析函数族.给出A的子族.DM g(α,β)={f(z)∈A:Re{z(f*g)'(z)/(f*g)(z)}<β|z(f*g)'(z)/(f*g)(z)-1|+α,g(z)∈A},这里α>1,β≤0,介绍了一类积分算子函数I n(z)及其特殊类型的积分算子函数Ik n(z),G n(z),F n(z),利用解不等式的技巧和解析函数理论,研究得到了一些它们的性质,推广了一些已有的结论.

A is denoted the class of functions which is univalent and analytic in the open unit disc U={z：〖JB（｜〗z〖JB）｜〗1,β≤0 is introduced. One integral operator In（z） and its special types Ikn（z）, Gn（z）, Fn（z） are also introduced. Some properties involving these operators are determined by using solutions of inequalities techniques and theories of analytic functions. The sharp results generalize some known results.