Subordination by convex functions - Rosihan M. Ali; V. Ravichandran; N. Seenivasagan (International Journal of Mathematics and Mathematical Sciences)
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.