Some applications of differential subordination

The authors introduce a two-parameter function G(p,λ;z)G(p,λ;z) which is shown to play an important rôle in a unified presentation of many interesting subclasses of analytic and pp-valent functions in the open unit disk UU. Making use of the familiar principle of differential subordination, several properties and relationships involving the function G(p,λ;z)G(p,λ;z) are derived. Some sufficient conditions for pp-valent starlikeness are also obtained.