Close-To-Convexity and Starlikeness of Analytic Functions

For functions f (z) = z^p +a_n+_1z^(p+1)+... defined on the open unit disk, the condition Re(f'(z)/z^(p−1)) ＞ 0 is sufficient for close-to-convexity of f . By making use of this result, several sufficient conditions for close-to-convexity are investigated and relevant connections with previously known results are indicated.