Certain Results on Starlike and Parabolic Starlike Functions

Abstract

Using the technique of differential subordination, we obtain certain results for starlike and parabolic starlike functions involving the differential operator zf ′(z) f(z) ( 1 + α zf ′′(z) f ′(z) ) . We study the above operator for multivalent functions and also conclude some results for univalent functions.