International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 19, Pages 62548, 6 p.
doi:10.1155/IJMMS/2006/62548
Subordination by convex functions
Rosihan M. Ali
, V. Ravichandran
and N. Seenivasagan
School of Mathematical Sciences, Universiti Sains Malaysia (USM), Penang 11800, Malaysia
Abstract
For a fixed analytic function g(z)=z+∑n=2∞gnzn defined on the open unit disk and γ<1, let Tg(γ) denote the class of all analytic functions f(z)=z+∑n=2∞anzn satisfying ∑n=2∞|angn|≤1−γ. For functions in Tg(γ), a subordination result is derived involving the convolution with a normalized convex function. Our result includes as special cases several earlier works.