On Sufficient Conditions for p-Valently Starlikeness and Strong Starlikness

Abstract:

      Let $A_{n}(p)~(p,n\in N=\{1,2,3,\cdots\})$ denote the class of functions of the form $f(z)=z^{p}+a_{p+n}z^{p+n}+\cdots$ that are analytic in the unit disk $E=\{z:|z|<1\}$. By using the method of differential subordinations we give some sufficient conditions for a function $f(z)\in A_{n}(p)$ to be $p$-valently starlike or strong starlike.