In this paper, we obtain some subordination results for certian subclasses of univalent functions defined by convolution.

Let $C_0(alpha)$ denote the class of concave univalent functions defined in the open unit disk $mathbb{D}$. Each function $f in C_{0}(alpha)$ maps the unit disk $mathbb{D}$ onto the complement of an unbounded convex set. In this paper, we study the mapping properties of this class under integral operators.

Virasoro algebra possesses a representation in the tangent space to the space of normalized univalent functions defined in the unit disk and smooth on its boundary. We discuss connections between representations of the Virasoro algebra and the Löwner-Kufarev equations in partial and ordinary derivatives. Virasoro generators turn to be conservative quantites for the Löwner-Kufarev ODE, and the L...

Let / be a function analytic in the unit disc, properly normalized, with bounded boundary rotation. There exists a Stieltjes integral representation for 1 +zf"(z)jf'(z). From this representation, and in view of a known variational formula for functions of positive real part, a variational formula is derived for functions of the form q(z) = l +zf"(z)jf'(z). This formula is for functions of arbit...

In this paper, we investigate necessary and sufficient coefficient conditions, distortion bounds, extreme points and convex combination of a new subclass of harmonic univalent functions defined by a generalization of modified Salagean operator. 2000 Mathematics Subject Classification: 30C45, 30C50. 1.Introduction Let H denote the family of continuous complex valued harmonic functions which are ...

In this paper we introduce some new subclasses of the class σ of bi-univalent functions and obtain bounds for the initial coefficients of the Taylor series expansion of functions from the considered classes.

In this paper, we define a new subclass Ao(A, B) of univalent functions and investigate several interesting characterization theorems involving a general class S" [A, B] of starlike functions