in this paper, we consider a new class of analytic functions in the unit disk using polynomials of order alpha. we give some sufficient conditions for functions belonging to this class.

We introduce new classes of q−starlike and q−convex functions of complex order with respect to (j, k)−symmetric points. Furthermore, the application of the results are also illustrated. We find estimates on the coefficients for second and third coefficients of these classes. Mathematics Subject Classification (2010): 30C45.

The purpose of the present paper is to establish some results concerning the partial sums of meromorphic starlike and meromorphic convex functions analogous to the results due to H. Silverman [J. Math. Anal. Appl. 209 (1997), 221-227]. Furthermore, we consider the partial sums of certain integral operator.

1. In addition to the study devoted to the general class of normalized regular univalent functions in the unit circle considerable attention has been given to certain subclasses of these functions such as starlike functions, convex functions, and others. In view of the important role played by symmetrization methods in recent work it seems worth while to study a further subclass—the class of ci...

Abstract The main objective of this paper is to obtain necessary and sufficient condition for a subclass of uniformly convex functions and corresponding subclass of starlike functions with fixed second coefficient defined by Carlson and Shaffer operator for the function f(z) in UCT (α, β). Furthermore, we obtain extreme points, distortion bounds and closure properties for f(z) in UCT (α, β) by ...

In this paper, we introduce a family of harmonic parabolic starlike functions of complex order in the unit disc and coefficient bounds, distortion bounds, extreme points, convolution conditions and convex combination are determined for functions in this family. Further results on integral transforms are discussed. Consequently, many of our results are either extensions or new approaches to thos...