The convolution of convex harmonic univalent functions in the unit disk, unlike analytic functions, may not be or even univalent. main purpose this work is to develop previous in...

Sufficient coefficient conditions for complex functions to be close-to-convex harmonic or convex harmonic are given. Construction of close-to-convex harmonic functions is also studied by looking at transforms of convex analytic functions. Finally, a convolution property for harmonic functions is discussed. Harmonic, Convex, Close-to-Convex, Univalent.

In this paper, we introduce some classes of univalent harmonic functions with respect to the symmetric conjugate points by means subordination, analytic parts which are reciprocal starlike (or convex) functions. Further, combining graph function, discuss bound Bloch constant and norm pre-Schwarzian derivative for classes.

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 ∈...

A function is said to be bi-univalent on the open unit disk D if both the function and its inverse are univalent in D. Not much is known about the behavior of the classes of bi-univalent functions let alone about their coefficients. In this paper we use the Faber polynomial expansions to find coefficient estimates for four well-known classes of bi-univalent functions which are defined by subord...

Also let S, S∗ β , CV β , and K denote, respectively, the subclasses of A0 consisting of functions which are univalent, starlike of order β, convex of order β cf. 1 , and close-to-convex cf. 2 in U. In particular, S∗ 0 S∗ and CV 0 CV are the familiar classes of starlike and convex functions in U cf. 2 . Given f and g inA, the function f is said to be subordinate to g in U if there exits a funct...

"A normalized function $f$ on the open unit disc is starlike (or convex) univalent if associated $zf'(z)/f(z)$ $1+zf''(z)/f'(z)$) a with positive real part. The radius of starlikeness or convexity usually obtained by using estimates for functions Using subordination, we examine various starlikeness, in particular, radii Janowski and order $\beta$, when either convex $(zf'(z)+\alpha z^2f''(z))/f...

We show that the univalent local actions of the complexification of a compact connected Lie group K on a weakly pseudoconvex space where K is acting holomorphically have a universal orbit convex weakly pseudoconvex complexification. We also show that if K is a torus, then every holomorphic action of K on a weakly pseudoconvex space extends to a univalent local action of KC.