单叶函数论中的螺旋形函数

Demonstrations on spirial function in univalents function

基于函数An、函数族Sn,mλ(A,B)、f(z)从属于g(z)以及λ-螺旋形函数的定义,给出了某些实数对函数的从属性,并证明了Re[(Dmf(z)/z)βeiλ]的精确下界,得出了几个推论,即:若f(z)是α阶星函数,则Re(f(z)/z)β>2-2β(1-α);若f(z)是α阶凸函数,则有Re(f′(z))β>2-2β(1-α)(0<β<2(1-α)-1)。同时,又用类似的方法证明了两族函数的包含关系,并就特殊情况做了系数估计,改进了前人的研究结果。

Based on function Ao ,function families Sn^λ m（A, B） ,the dependency off（z） to g（z） and the definition of λ-spirial function, the depedency of function and the greatest lower bound of Re[ （Dmf（z）/z）^βeiλ] were demonstrated,and some conclusions were drawn i.e. iff（z） is or-stage star function, Re（f（z）/z）β 〉2-2β（1-α） ; iff（z） is s-stage convex function, then Re（f ＇（z） ）β 〉2-2β（1-α） （0 〈β 〈2（ 1 - α） ^-1 ）. Besides, the inclusion relation between the two families of functions was demonstrated, and two additional conclusion were drawn. Finally, the former results were improved by way of coefficient estimation based on special case.