Let S*_LC represent a new subclass of analytic functions f defined in the open unit disk in the complex plane such that $\frac{zf’(z)}{f(z)}$ lies in the interior of the domain bounded by the limacon given by the equation (4x²+4y²−8x−5)²+8(4x²+4y²−12x−3)=0. In this paper, we investigate the geometric properties of functions in this class.

We consider meromorphic starlike univalent functions that are also bi-starlike and find Faber polynomial coefficient estimates for these types of functions. A function is said to be bi-starlike if both the function and its inverse are starlike univalent.

In [7], Sakaguchi introduce the class of functions starlike with respect to symmetric points. We extend this class. For p ≤ β < 1, let be the class of normalised analytic functions f defined in the open unit disc D such that Rezf^′(z)/(f(z) − f(−z)) > β, for some z ϵ D. In this paper, we introduce 2 other similar classes , as well as give sharp results for the real part of some function for , and The behaviour of certain integral operators are also considered.

A class $ S_{s}^{\star}T(\alpha,\beta,\sigma,k) $ of functions $ f $ which are analytic and univalent in the open unit disk $ {D=\{z:|z|