Suppose f is an almost starlike function of order α on the unit disk D. In this paper, we will prove that Фn,β2,γ2,…βn,γn（f）（z）=（f（z1）,（f（z1）/z1）^β2（f＇（z1））^γ2 z2,…,（f（z1）/z1）^βn（f＇（z...Suppose f is an almost starlike function of order α on the unit disk D. In this paper, we will prove that Фn,β2,γ2,…βn,γn（f）（z）=（f（z1）,（f（z1）/z1）^β2（f＇（z1））^γ2 z2,…,（f（z1）/z1）^βn（f＇（z1））^γnzn）1 preserves almost starlikeness of order α on Ωn,p2,…,pn={z=（z1,z2,…,zn）＇∈Cn：∑^n j=1｜zj｜^pj〈1},where 0〈p1≤2,pj≥1,j=2,…,n,are real numbers.展开更多
基金Supported by the National Natural Science Foundation of China(10626015,10571044)Supported by the Guangdong Natural Science Foundation(06301315)+1 种基金Supported by the Doctoral Foundation of Zhanjiang Normal University(Z0420)Supported by the Natural Science Foundation of Henan University(XK03YBSX200)
文摘Suppose f is an almost starlike function of order α on the unit disk D. In this paper, we will prove that Фn,β2,γ2,…βn,γn（f）（z）=（f（z1）,（f（z1）/z1）^β2（f＇（z1））^γ2 z2,…,（f（z1）/z1）^βn（f＇（z1））^γnzn）1 preserves almost starlikeness of order α on Ωn,p2,…,pn={z=（z1,z2,…,zn）＇∈Cn：∑^n j=1｜zj｜^pj〈1},where 0〈p1≤2,pj≥1,j=2,…,n,are real numbers.
