scholarly journals The Distortion Theorems for Harmonic Mappings with Analytic Parts Convex or Starlike Functions of Orderβ

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Mengkun Zhu ◽  
Xinzhong Huang
Keyword(s):  
Starlike Functions ◽  
Harmonic Mappings ◽  
Sharp Estimates ◽  
Covering Theorems ◽  
Distortion Theorems

Some sharp estimates of coefficients, distortion, and growth for harmonic mappings with analytic parts convex or starlike functions of orderβare obtained. We also give area estimates and covering theorems. Our main results generalise those of Klimek and Michalski.

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 $\overline{HS}(k,\lambda,b,\alpha)$.

Harmonic mappings related to the m-fold starlike functions

2015 ◽  
Vol 267 ◽  
pp. 805-809
Author(s):  
Melike Aydoğan ◽  
Yaşar Polatoğlu ◽  
Yasemin Kahramaner
Keyword(s):  
Starlike Functions ◽  
Harmonic Mappings

scholarly journals Harmonic mappings related to Janowski starlike functions

2014 ◽  
Vol 270 ◽  
pp. 564-570
Author(s):  
Yasemin Kahramaner ◽  
Yaşar Polatog˜lu ◽  
Melike Aydog˜an
Keyword(s):  
Starlike Functions ◽  
Harmonic Mappings

Applications on a subclass of β-uniformly starlike functions connected with q-Borel distribution

2021 ◽  
Author(s):  
Sheza M. El-Deeb ◽  
G. Murugusundaramoorthy
Keyword(s):  
Starlike Functions ◽  
Coefficient Estimates ◽  
Linear Combinations ◽  
Distortion Theorems ◽  
Uniformly Starlike Functions ◽  
Uniformly Starlike

The aim of this paper is to define the operator of [Formula: see text]-derivative based upon the Borel distribution and by using this operator, we familiarize a new subclass of [Formula: see text]-uniformly starlike functions [Formula: see text]-[Formula: see text] Further, we obtain coefficient estimates, distortion theorems, convex linear combinations and radii of close-to-convexity, starlikeness and convexity for functions [Formula: see text]-[Formula: see text] We also determine the second Hankel inequality for functions belonging to this subclass.

scholarly journals Harmonic Starlike Functions with Respect to Symmetric Points

Axioms ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 3 ◽  
Author(s):  
Nak Eun Cho ◽  
Jacek Dziok
Keyword(s):  
Integral Representation ◽  
Starlike Functions ◽  
Coefficient Estimates ◽  
Distortion Theorems ◽  
Harmonic Starlike ◽  
Symmetric Points

In the paper we define classes of harmonic starlike functions with respect to symmetric points and obtain some analytic conditions for these classes of functions. Some results connected to subordination properties, coefficient estimates, integral representation, and distortion theorems are also obtained.

scholarly journals Distortion and covering theorems of pluriharmonic mappings

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2749-2762
Author(s):  
Shaolin Chen ◽  
Saminathan Ponnusamy
Keyword(s):  
Analytic Functions ◽  
Harmonic Mappings ◽  
Classical Approach ◽  
Covering Theorems ◽  
Linear Invariant ◽  
Planar Harmonic Mappings

The linear-invariant families of analytic functions make it possible to obtain well-known results to broader classes of functions, and are often helpful in obtaining simpler proofs along with new results. Based on this classical approach due to Pommerenke, properties (such as bounds for the derivative, covering and distortion) of a corresponding class of locally quasiconformal and planar harmonic mappings are established by Starkov. Motivated by these works, in this paper, we mainly investigate distortion and covering theorems on some classes of pluriharmonic mappings.

scholarly journals The Sharp Bound of the Hankel Determinant of the Third Kind for Starlike Functions with Real Coefficients

2019 ◽  
Author(s):  
Oh Sang Kwon ◽  
Young Jae Sim
Keyword(s):  
Analytic Functions ◽  
Starlike Functions ◽  
Sharp Bound ◽  
Hankel Determinant ◽  
Sharp Estimates ◽  
The Third

Let ${\mathcal{SR}}^*$ be the class of starlike functions with real coefficients, i.e., the class of analytic functions $f$ which satisfy the condition $f(0)=0=f'(0)-1$, Re{z f'(z) / f (z)} > 0, for $z\in\mathbb{D}:=\{z\in\mathbb{C}:|z|<1 \}$ and $a_n:=f^{(n)}(0)/n!$ is real for all $n\in\mathbb{N}$. In the present paper, the sharp estimates of the third Hankel determinant $H_{3,1}$ over the class ${\mathcal{SR}}^*$ are computed.

scholarly journals Some General Classes of q-Starlike Functions Associated with the Janowski Functions

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 292 ◽  
Author(s):  
Hari Srivastava ◽  
Muhammad Tahir ◽  
Bilal Khan ◽  
Qazi Ahmad ◽  
Nazar Khan
Keyword(s):  
Unit Disk ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Janowski Functions ◽  
Distortion Theorems ◽  
The Relationship

By making use of the concept of basic (or q-) calculus, various families of q-extensions of starlike functions of order α in the open unit disk U were introduced and studied from many different viewpoints and perspectives. In this paper, we first investigate the relationship between various known classes of q-starlike functions that are associated with the Janowski functions. We then introduce and study a new subclass of q-starlike functions that involves the Janowski functions. We also derive several properties of such families of q-starlike functions with negative coefficients including (for example) distortion theorems.

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