Some properties of starlike functions with respect to symmetric-conjugate points

International Journal of Mathematics and Mathematical Sciences

卷:18

HassoonAl-Amiri¹  Dancoman²  Petru T. Mocanu³ 

[1] Department ofMathematics and Statistics, Bowling Gteen State Uiversity, Bowling Gteen 43403, Ohio, USA;

[2] Departnent of Mathematics, University of Michigan, Ann Arbor 48109, MI, USA;

[3] Faculty of Mathematics, Babes-Bolyai University, Cluj-Napoca 3400, Romania;

关键词: symmetric-conjugate points;    starlike;    differential subordinations;    integral operator;    strongly starlike;    α;    -convex.;   

DOI  :  10.1155/S0161171295000597

来源: DOAJ

【 摘 要 】

Let A be tile class of all analytic functions in the unit disk U such that f(0)=f′(0)−1=0. A function f∈A is called starlike with respect to 2n symmetric-conjugate pointsif Rezf′(z)/fn(z)>0 for z∈U, wherefn(z)=12n∑k=0n−1[ω−kf(ωkz)+ωkf(ωkz˜)¯],ω=exp(2πi/n]. This class is denoted by Sn*, and was studied in [1]. A sufficient condition forstarlikeness with respect to symmetric-conjugate points is obtained. In addition, images of somesubclasses of Sn* under the integral operator I:A→A, I(f)=F whereF(z)=c+1(g(z))c∫0zf(t)(g(t))c−1g′(t)dt,   c>0and g∈A is given are determined.

【 授权许可】

Unknown