In this paper, we investigate the sharp bounds of second Hankel determinant Logarithmic coefficients for starlike and convex functions with respect to symmetric points in open unit disk.

The theory of geometric functions was first introduced by Bernard Riemann in 1851. In 1916, with the concept normalized function revealed Bieberbach, univalent has found application area. Assume f(z)=z+??, n?(anzn) converges for all complex numbers z |z|<1 and f(z)is one-to-one on set such z. Convex starlike f(z) g(z) are discussed help subordination. analytic unit disc f(0)=f'(0)=1, g(0)=0,...

In this paper, we define a generalized class of starlike functions with negative coefficients and obtain coefficient estimates, distortion bounds, closure theorems and extreme points. Further we obtain modified Hadamard product, radii of close-to-convex, starlikeness and convexity for functions belonging to this class. Furthermore neighborhood results are discussed.

Let A(ω) be the class of analytic functions of the form: f(z) = (z − ω) + ∞ ∑ k=2 ak(z − ω) defined on the open unit disk U = {z : |z| < 1} normalized with f(ω) = 0, f ′(ω)−1 = 0 and ω is an arbitrary fixed point in U. In this paper, we define a subclass of ω − α − uniform starlike and convex functions by using a more generalized form of Ruschewey derivative operator. Several properties such as...

An interesting criterion was given by Tuneski [N. Tuneski, On the quotient of the representations of convexity and starlikeness, Math. Nachr. 248–249 (2003) 200–203] for the analytic functions to be in the class S 1⁄21þAz 1þBz and its subclasses, where 1 6 B < A 6 1. This result is an extension of an earlier result of Silverman [H. Silverman, Convex and starlike criteria, Int. Math. Math. Sci. ...

Making use of Linear operator theory, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients. The main object of this paper is to obtain coefficient estimates distortion bounds, closure theorems and extreme points for functions belonging to this new class. The results are generalized to families with fixed finitely ma...