Some characteristic properties of analytic functions

In this paper, we consider a class L(lambda, mu; phi) of analytic functions f defined in the open unit disk U satisfying the subordination condition that q(z)D lambda vertical bar f(z) / D lambda f (z) < phi(z) (lambda is an element of N-0,N- mu >= 0; z is an element of U), where q(z) = (z/D lambda f(z))(mu-2) , D-lambda is the Salagean operator and phi(z) is a convex function with positive real part in U. We obtain some characteristic properties giving the coefficient inequality, radius and subordination results, and an inclusion result for the above class when the function phi(z) is a bilinear mapping in the open unit disk. For these functions f (z), sharp bounds for the initial coefficient and for the Fekete-Szego functional are determined, and also some integral representations are given.