scholarly journals Subclass of Harmonic Univalent Functions Associated with the Generalized Mittag-Leffler Type Functions

2020 ◽  
pp. 139-153
Author(s):  
Adnan Ghazy Alamoush
Keyword(s):  
Unit Disc ◽  
Harmonic Functions ◽  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Distortion Bounds

In the present paper, we introduce a new subclass of harmonic functions in the unit disc U defined by using the generalized Mittag-Leffler type functions. Coefficient conditions, extreme points, distortion bounds, convex combination are studied.

scholarly journals A Brief Study of Certain Class of Harmonic Functions of Bazilevič Type

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
A. T. Oladipo ◽  
D. Breaz
Keyword(s):  
Linear Operator ◽  
Harmonic Functions ◽  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Distortion Bounds

We define and investigate a new subclass of Bazilevič type harmonic univalent functions using a linear operator. We investigated the harmonic structures in terms of its coefficient conditions, extreme points, distortion bounds, convolution, and convex combination. So, also, we discussed the subordination properties for the functions in this class.

scholarly journals A New Subclass of Salagean-Type Harmonic Univalent Functions

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Khalifa Al-Shaqsi ◽  
Maslina Darus ◽  
Olubunmi Abidemi Fadipe-Joseph
Keyword(s):  
Harmonic Functions ◽  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Distortion Bounds

We define and investigate a new subclass of Salagean-type harmonic univalent functions. We obtain coefficient conditions, extreme points, distortion bounds, convolution, and convex combination for the above subclass of harmonic functions.

scholarly journals A subclass of harmonic univalent functions with positive coefficients

2010 ◽  
Vol 41 (3) ◽  
pp. 261-269 ◽  
Author(s):  
K. K. Dixit ◽  
Saurabh Porwal
Keyword(s):  
Integral Operator ◽  
Unit Disc ◽  
Harmonic Functions ◽  
Univalent Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Open Unit Disc ◽  
Distortion Bounds ◽  
Positive Coefficients ◽  
Complex Valued

Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disc $U$ can be written in the form $f=h+\bar g$, where $h$ and $g$ are analytic in $U$. In this paper authors introduce the class, $R_H(\beta)$, $(1<\beta \le 2)$ consisting of harmonic univalent functions $f=h+\bar g$, where $h$ and $g$ are of the form $ h(z)=z+ \sum_{k=2}^\infty |a_k|z^k $ and $ g(z)= \sum_{k=1}^\infty |b_k| z^k $ for which $\Re\{h'(z)+g'(z)\}<\beta$. We obtain distortion bounds extreme points and radii of convexity for functions belonging to this class and discuss a class  preserving integral operator. We also show that class studied in this paper is closed under convolution and convex combinations.

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

scholarly journals On Certain Subclass of Harmonic Starlike Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
A. Y. Lashin
Keyword(s):  
Integral Operator ◽  
Unit Disc ◽  
Univalent Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
New Class ◽  
Distortion Bounds ◽  
Harmonic Starlike

Coefficient conditions, distortion bounds, extreme points, convolution, convex combinations, and neighborhoods for a new class of harmonic univalent functions in the open unit disc are investigated. Further, a class preserving integral operator and connections with various previously known results are briefly discussed.

scholarly journals On (p,q)-Starlike Harmonic Functions Defined By Subordination

2021 ◽  
Vol 26 (4) ◽  
pp. 491-500
Author(s):  
Hasan BAYRAM ◽  
Sibel Yalçın
Keyword(s):  
Harmonic Functions ◽  
Univalent Functions ◽  
Extreme Points ◽  
Distortion Bounds ◽  
Necessary And Sufficient

We introduce and investigate classes of (p,q)-starlike harmonic univalent functions defined by subordination. We first obtained a coefficient characterization of these functions. We give necessary and sufficient convolution conditions, distortion bounds, compactness and extreme points for the (p,q)-starlike harmonic univalent with negative coefficients.

scholarly journals A New Subclass of Harmonic Univalent Functions Associated with Dziok-Srivastava Operator

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
A. L. Pathak ◽  
K. K. Dixit ◽  
R. Agarwal
Keyword(s):  
Integral Operator ◽  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Distortion Bounds

The purpose of the present paper is to study a certain subclass of harmonic univalent functions associated with Dziok-Srivastava operator. We obtain coefficient conditions, distortion bounds, and extreme points for the above class of harmonic univalent functions belonging to this class and discuss a class preserving integral operator. We also show that class studied in this paper is closed under convolution and convex combination. The results obtained for the class reduced to the corresponding results for several known classes in the literature are briefly indicated.

scholarly journals Subclass of Multivalent Harmonic Functions Defi…ned by Wright Generalized Hypergeometric Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
M. K. Aouf ◽  
A. O. Moustafa ◽  
E. A. Adwan
Keyword(s):  
Harmonic Functions ◽  
Hypergeometric Functions ◽  
Convex Combination ◽  
Extreme Points ◽  
Coefficient Estimates ◽  
Generalized Hypergeometric Functions ◽  
New Class ◽  
Function Coefficient ◽  
Distortion Bounds ◽  
Wright Generalized Hypergeometric Functions

We introduce a new class of multivalent harmonic functions defi…ned by Wright generalized hypergeometric function. Coefficient estimates, extreme points, distortion bounds, and convex combination for functions belonging to this class are obtained.

scholarly journals Subclasses of Harmonic Mappings Defined by Convolution

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Santosh B. Joshi ◽  
Girish D. Shelake
Keyword(s):  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Harmonic Mappings ◽  
Coefficient Bounds ◽  
Integral Convolution ◽  
Distortion Bounds ◽  
Special Cases

Two new subclasses of harmonic univalent functions defined by using convolution and integral convolution are introduced. These subclasses generate several known and new subclasses of harmonic univalent functions as special cases and provide a unified treatment in the study of these classes. Coefficient bounds, extreme points, distortion bounds, convolution conditions, and convex combination are also determined.

scholarly journals Properties of a Class of -Harmonic Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Elif Yaşar ◽  
Sibel Yalçın
Keyword(s):  
Differential Operator ◽  
Positive Integer ◽  
Harmonic Functions ◽  
Convex Combination ◽  
Extreme Points ◽  
Distortion Bounds ◽  
Harmonic Equation ◽  
Necessary And Sufficient ◽  
Complex Valued

A times continuously differentiable complex-valued function in a domain is -harmonic if satisfies the -harmonic equation , where is a positive integer. By using the generalized Salagean differential operator, we introduce a class of -harmonic functions and investigate necessary and sufficient coefficient conditions, distortion bounds, extreme points, and convex combination of the class.

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