scholarly journals On the Generalization of a Class of Harmonic Univalent Functions Defined by Differential Operator

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 312
Author(s):  
Aqeel Ketab AL-khafaji ◽  
Waggas Galib Atshan ◽  
Salwa Salman Abed
Keyword(s):  
Differential Operator ◽  
Hadamard Product ◽  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Coefficient Estimates ◽  
Geometric Properties ◽  
New Class

In this article, a new class of harmonic univalent functions, defined by the differential operator, is introduced. Some geometric properties, like, coefficient estimates, extreme points, convex combination and convolution (Hadamard product) are obtained.

scholarly journals A Class of Harmonic Univalent Functions Defined by Differential Operator and the Generalization

2020 ◽  
pp. 1440-1445
Author(s):  
Faten Fakher Aubdulnabi ◽  
Kassim A. Jassim
Keyword(s):  
Differential Operator ◽  
Hadamard Product ◽  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Coefficient Estimates ◽  
Geometric Properties ◽  
New Class

In this paper, a new class of harmonic univalent functions was defined by the differential operator. We obtained some geometric properties, such as the coefficient estimates, convex combination, extreme points, and convolution (Hadamard product), which are required

scholarly journals A class of harmonic functions associated with a generalized differential operator

2020 ◽  
Vol 108 (122) ◽  
pp. 145-154
Author(s):  
Sarika Verma ◽  
Deepali Khurana ◽  
Raj Kumar
Keyword(s):  
Differential Operator ◽  
Harmonic Functions ◽  
Univalent Functions ◽  
Extreme Points ◽  
Coefficient Estimates ◽  
Geometric Properties ◽  
New Class ◽  
Inclusion Relations ◽  
Generalized Differential

We introduce a new class of harmonic univalent functions by using a generalized differential operator and investigate some of its geometric properties, like, coefficient estimates, extreme points and inclusion relations. Finally, we show that this class is invariant under Bernandi-Libera-Livingston integral for harmonic functions.

scholarly journals Some Geometric Properties for a Certain Class of Meromorphic Univalent Functions by Differential Operator

2021 ◽  
pp. 2667-2675
Author(s):  
Mohammed Hadi Lafta
Keyword(s):  
Differential Operator ◽  
Hadamard Product ◽  
Convex Combination ◽  
Univalent Functions ◽  
Integral Operators ◽  
Coefficient Estimates ◽  
Growth Theorem ◽  
Closure Theorem ◽  
Major Target ◽  
Meromorphic Univalent Functions

The major target of this paper is to study a confirmed class of meromorphic univalent functions . We procure several results, such as those related to coefficient estimates, distortion and growth theorem, radii of starlikeness, and convexity for this class, n additionto hadamard product, convex combination, closure theorem, integral operators, and  neighborhoods.

scholarly journals New Family of Multivalent Analytic Functions Defined on Complex Hilbert Space

2020 ◽  
pp. 155-165 ◽  
Author(s):  
Abbas Kareem Wanas ◽  
S. R. Swamy
Keyword(s):  
Hilbert Space ◽  
Analytic Functions ◽  
Convex Set ◽  
Extreme Points ◽  
Complex Hilbert Space ◽  
Coefficient Estimates ◽  
Geometric Properties ◽  
New Class ◽  
New Family

In this article, we define a certain new class of multivalent analytic functions with negative coefficients on complex Hilbert space. We derive a number of important geometric properties, such as, coefficient estimates, radii of starlikeness and convexity, extreme points and convex set.

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 Applications of Fractionalq-Calculus to Certain Subclass of Analyticp-Valent Functions with Negative Coefficients

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Ben Wongsaijai ◽  
Nattakorn Sukantamala
Keyword(s):  
Differential Operator ◽  
Convex Function ◽  
Extreme Points ◽  
Negative Coefficient ◽  
Geometric Properties ◽  
New Class ◽  
General Properties ◽  
Inclusion Relations ◽  
Invariant Properties

By making use of the concept of fractionalq-calculus, we firstly defineq-extension of the generalization of the generalized Al-Oboudi differential operator. Then, we introduce new class ofq-analogue ofp-valently closed-to-convex function, and, consequently, new class by means of this new general differential operator. Our main purpose is to determine the general properties on such class and geometric properties for functions belonging to this class with negative coefficient. Further, theq-extension of interesting properties, such as distortion inequalities, inclusion relations, extreme points, radii of generalized starlikeness, convexity and close-to-convexity, quasi-Hadamard properties, and invariant properties, is obtained. Finally, we briefly indicate the relevant connections of our presented results to the former results.

A New Subclass of Harmonic Univalent Functions

2017 ◽  
Vol 9 (2) ◽  
pp. 26-32
Author(s):  
Waggas Galib Atshan ◽  
Najah Ali Jiben Al-Ziadi
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Bounds ◽  
Basic Properties ◽  
New Class

In this paper, we define a new class of harmonic univalent functions of the form  in the open unit disk . We obtain basic properties, like, coefficient bounds, extreme points, convex combination, distortion and growth theorems and integral operator.

scholarly journals On A Subclass of Harmonic Univalent Funtions Associated with the Differential Operator

2018 ◽  
Vol 7 (3.3) ◽  
pp. 138
Author(s):  
B Ravindar ◽  
R Bharavi Sharma
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Univalent Functions ◽  
Extreme Points ◽  
Coefficient Estimates

In this paper, a new subclass of harmonic univalent functions in the unit disk  is introduced using a differential operator. Also the coefficient estimates, convolution conditions, extreme points and convex combinations are obtained.  

scholarly journals A Certain Subclass of Analytic and Univalent Functions Defined by Hadamard Product

2019 ◽  
pp. 87-99
Author(s):  
Dhirgam Allawy Hussein ◽  
Sahar Jaafar Mahmood
Keyword(s):  
Hadamard Product ◽  
Univalent Functions ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Radius Of Starlikeness ◽  
Closure Theorems ◽  
Analytic And Univalent Functions

In this paper, we present a new subclass AD(l, g, a, b) of analytic univalent functions in the open unit disk U. We establish some interesting properties like, coefficient estimates, closure theorems, extreme points, growth and distortion theorem and radius of starlikeness and convexity.

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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