- 期刊
SUBCLASSES OF CLOSE-TO-CONVEX FUNCTIONS
摘要
Let K[C,D], -1 ≤ D ＜ C ≤ 1, denote the class of functions g(z), g(0)=g'(0)-1=0, analytic in the unit disk U={z:|z|＜1} such that 1+(zg''(z)/g'(z)) is subordinate to (1+Cz)/(1+Dz), z ϵ U. We investigate the subclasses of close-to-convex functions f(z), f(0)=f'(0)-1=0, for which there exists g ϵ K[C,D] such that f'/g' is subordinate to(1+Az)/(1+Bz), -1 ≤ B ＜ A ≤ 1. Distortion and rotation theorems and coefficient bounds are obtained. It is also shown that these classes are preserved under certain integral operators.
延伸閱讀
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