Harmonic univalent functions with fixed second coefficient

On Univalent Harmonic Functions

Two classes of univalent harmonic functions on unit disc satisfying the conditions ∑∞ n=2(n−α)(|an|+|bn|) ≤ (1−α)(1−|b1|) and ∑∞ n=2 n(n−α)(|an|+|bn|) ≤ (1−α)(1−|b1|) are given. That the ranges of the functions belonging to these two classes are starlike and convex, respectively. Sharp coefficient relations and distortion theorems are given for these functions. Furthermore results concerning th...

Univalent Harmonic Functions

A necessary and sufficient coefficient is given for functions in a class of complexvalued harmonic univalent functions using the Dziok-Srivastava operator. Distortion bounds, extreme points, an integral operator, and a neighborhood of such functions are considered.

Coefficient Estimates for Univalent Functions

Coefficient ConditionsFor Certain Univalent Functions

Some subclasses of analytic functions f(z) in the open unit disk U are introduced. In the present paper, Some interesting sufficient conditions, including coefficient inequalities related close-to-convex functions f(z) of order α with respect to a fixed starlike function g(z) and strongly starlike functions f(z) of order μ in U, are discussed. Several special cases and consequences of these coe...

Radius Constants for Analytic Functions with Fixed Second Coefficient

Let f(z) = z + ∑(n=2)(∞) (a)n(z) (n) be analytic in the unit disk with the second coefficient a2 satisfying |a2| = 2b, 0 ≤ b ≤ 1. Sharp radius of Janowski starlikeness is obtained for functions f whose nth coefficient satisfies |a(n)| ≤ cn + d (c, d ≥ 0) or |a(n)| ≤ c/n  (c > 0 and n ≥ 3). Other radius constants are also obtained for these functions, and connections with earlier results are made.