Gegenbauer polynomials for certain subclasses of Bazilevic functions associated with a generalized operator defined by convolution

Abstract

In this paper, a class G_{η_1,η_2}^β(α,t), consisting of Bazilevic functions of type α and involving a certain generalized differential operator is defined by means of Gegenbauer polynomials. Initial coefficient bounds and Fekete-Szego estimates for functions belonging to this class are obtained. Furthermore, upon varying the involving parameters  in our main results, a number of known and new results are stated as corollaries.