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

Let AA be the class of functions f:f(z)=z+∑n=2∞anzn, which are analytic in the open unit disc EE. We use a linear operator closely related to the multiplier transformation to introduce and investigate certain subclasses of AA which map EE 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.