Extremal properties of certain classes of univalent functions

1969 ◽  
pp. 251-264
Author(s):  
V. A. Pohilevič
Keyword(s):  
Univalent Functions ◽  
Extremal Properties

Some Problems for Typically Real Functions

1961 ◽  
Vol 13 ◽  
pp. 299-304 ◽  
Author(s):  
James A. Jenkins
Keyword(s):  
Unit Circle ◽  
Univalent Functions ◽  
Real Functions ◽  
Representation Result ◽  
Typically Real ◽  
Typically Real Functions ◽  
Extremal Properties

Many extremal properties of the class of normalized univalent functions are shared by the class of typically real functions each considered in the unit circle. By the class T of typically real functions we mean those functions f(z), regular for |z| < 1 with f(0) = 0, f'(0) = 1, and such that f(z) > 0 for z > 0, (z) < 0 for > 0. This class was first studied by Rogosinski (4) who proved various simple properties for it. Later Robertson (3) took up the study and proved the following important representation result.

Certain Subclasses of Bi-Univalent Functions Involving Double Zeta Function

2015 ◽  
Vol 4 (4) ◽  
pp. 28-33
Author(s):  
Dr. T. Ram Reddy ◽  
◽  
R. Bharavi Sharma ◽  
K. Rajya Lakshmi ◽  
◽  
...  
Keyword(s):  
Zeta Function ◽  
Univalent Functions ◽  
Double Zeta

A Class of Harmonic Starlike Functions defined by Multiplier Transformation

2020 ◽  
pp. 455-469
Author(s):  
Deepali Khurana ◽  
Raj Kumar ◽  
Sibel Yalcin
Keyword(s):  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Harmonic Mappings ◽  
Distortion Bounds ◽  
Radius Of Convexity ◽  
Univalent Harmonic Mappings ◽  
Harmonic Starlike ◽  
Multiplier Transformation

We define two new subclasses, $HS(k, \lambda, b, \alpha)$ and \linebreak $\overline{HS}(k, \lambda, b, \alpha)$, of univalent harmonic mappings using multiplier transformation. We obtain a sufficient condition for harmonic univalent functions to be in $HS(k,\lambda,b,\alpha)$ and we prove that this condition is also necessary for the functions in the class $\overline{HS} (k,\lambda,b,\alpha)$. We also obtain extreme points, distortion bounds, convex combination, radius of convexity and Bernandi-Libera-Livingston integral for the functions in the class $\overline{HS}(k,\lambda,b,\alpha)$.

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