A cardioid domain and starlike functions

We introduce and study a class of starlike functions defined by S ℘ ∗ : = f ∈ A : z f ′ ( z ) f ( z ) ≺ 1 + z e z = : ℘ ( z ) , where ℘ maps the unit disk onto a cardioid domain. We find the radius of convexity of ℘ ( z ) and establish the inclusion relations between the class S ℘ ∗ and some well-known classes. Further we derive sharp radius constants and coefficient related results for the class S ℘ ∗ .