Let S ( A , B , p , α ) denote the class of functions g ( z ) = z p + ∑ n = p + 1 ∞ b n z n analytic in the unit disc U = { z : | z | < 1 } and satisfying the condition z g ′ ( z ) g ( z ) < p + [ p B + ( A − B ) ( p − α ) ] z 1 + B z ,       z ∈ U ,       − 1 ≦ B < A ≦ 1 ,       0 ≦ α < p . Let C ( A , B , p , β , α ) denote the class of functions f ( z ) = z p + ∑ n = p + 1 ∞ a n z n analytic in U , and satisfying the condition \beta ,z \in U,g \in S\left( {A,B,p,\alpha } \right).$" display="block"> Re { z f ′ ( z ) g ( z ) } > β ,     z ∈ U ,       g ∈ S ( A , B , p , α ) . In this paper we determine the coefficient estimates and distortion theorems for the class C ( A , B , p , β , α ) .