Applications of certain operators to the classes of analytic functions related with generalized conic domains

Let A be the class of functions f : f (z) = z + Sigma(infinity)(n=2) a(n)z(n), which are analytic in the open unit disc E. We use a linear operator closely related to the multiplier transformation to introduce and investigate certain subclasses of A which map E onto a generalized form of the conic domain. Several properties of these classes including some inclusion relations, convolution and other class preserving operators are studied. In particular, we derive many known and new results as special cases. Applications of some results are also given. (C) 2011 Elsevier Ltd. All rights reserved.