【摘要】 设函数在单位圆盘｜ｚ｜＜１内解析，且１，其中｛αｎ｝为一正实数序列．记具有这种性质的函数ｆ（ｚ）的全体为Ｓ（αｎ）．本文证明，如果ｆ（ｚ）∈Ｓ（αｎ），且αｎ≥［（ｎ－１）（αｐ－１）＋ｐ－１］／（ｐ－１），则ｆ（ｚ）为α阶星象函数，其中α＝（αｐ－ｐ）／（αｐ－１）．特殊情形，当αｎ＝ｎ，ｐ＝２时，Ｓ（ｎ）为众所周知的ＡＷ．Ｃｏｏｄｍａｎ（１９５７）关于原点的星象函数族，此外，本文还研究了Ｓ（αｎ）的单叶性条件，变形定理，旋转定理以及关于任意点为星象的条件，其中定理７和推论１推广了Ｈ．Ｓｉｌｖｅｒｍａｎ（１９５７）的一些结果．更多还原

【Abstract】 Let function be analytic in the unit disk|z|<1,and where{αn}is a sequence of positive real number.We denote the class of all functions f(z) with these properties by S(αn).This paper proves that ,if f(z)∈S(αn) and αn≥[(n-1)(αp-1)+p-1]/(p-1),then f(z) is starlike function of order αwhere α=(αp-p)/(αp-1).In particular cases,when p=2 and αn=n,we obtain class S(n)which is well-known one in Reference 6 of starlike functions. Furthermore,this paper also considers condition of univalence,distortion theorem,rotation theorem,and condition of starlikeness with respect to any point for class S(αn).The theorem 7 and corollarg 1 in this paper also are generalization of some results from Reference 7.更多还原