On univalent functions convex in one direction

Univalent Harmonic Mappings Convex in One Direction

In this work some distortion theorems and relations between the coefficients of normalized univalent harmonic mappings from the unit disc onto domains on the direction of imaginary axis are obtained.

Convex and Starlike Univalent Functions

Generating Starlike and Convex Univalent Functions

Alexander [1] was the first to introduce certain subclasses of univalent functions examining the geometric properties of the image f(D) of D under f . The convex functions are those that map D onto a convex set. A function w = f(z) is said to be starlike if, together with any of its points w, the image f(D) contains the entire segment {tw : 0 ≤ t ≤ 1}. Thus we introduce the denotations S = {f ∈...

On a Subclass of Quasi-Convex Univalent Functions

Abstract: The aim of this paper is to introduce and study a new class [ ] * C A,B, δ α of Janowski QuasiConvex univalent functions of order alpha associated with Ruscheweyh derivative. Sharp coefficient bound, distortion result and some inclusion results are discussed. Invariance of [ ] * C A,B, δ α under convolution with convex functions has also been examined and some of its applications are ...

Subclasses of Univalent Functions Subordinate to Convex Functions

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