scholarly journals Some Properties of a New Class of Univalent Functions Involving a New Generalized Differential Operator with Negative Coefficients

2016 ◽  
Vol 9 (36) ◽  
Author(s):  
A. Amourah ◽  
Maslina Darus
Keyword(s):  
Differential Operator ◽  
Univalent Functions ◽  
New Class ◽  
Generalized Differential

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 Univalent Functions Defined by a Generalized Multiplier Differential Operator

2019 ◽  
pp. 1-13
Author(s):  
Adnan Ghazy Alamoush
Keyword(s):  
Differential Operator ◽  
Univalent Functions ◽  
Alpha Beta ◽  
Generalized Differential

In this paper, we investigate a new subclass of univalent functions defined by a generalized differential operator, and obtain some interesting properties of functions belonging to the class R^{m}_{\lambda, \mu, \alpha, \beta, \gamma, \vartheta}(\varpi).

scholarly journals Some Properties of Complex Harmonic Mapping

2012 ◽  
Vol 2012 ◽  
pp. 1-6
Author(s):  
E. A. Eljamal ◽  
M. Darus
Keyword(s):  
Differential Operator ◽  
Harmonic Functions ◽  
Harmonic Mapping ◽  
New Class ◽  
Generalized Differential

We introduce new class of harmonic functions by using certain generalized differential operator of harmonic. Some results which generalize problems considered by many researchers are present. The main results are concerned with the starlikeness and convexity of certain class of harmonic functions.

scholarly journals Faber polynomial coefficients estimates for certain subclasses of $ q $-Mittag-Leffler-Type analytic and bi-univalent functions

2021 ◽  
Vol 7 (2) ◽  
pp. 2512-2528
Author(s):  
Zeya Jia ◽  
◽  
Nazar Khan ◽  
Shahid Khan ◽  
Bilal Khan ◽  
...  
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Univalent Functions ◽  
Expansion Method ◽  
Open Unit ◽  
Open Unit Disk ◽  
Faber Polynomial ◽  
Polynomial Coefficients ◽  
Polynomial Expansion Method ◽  
Generalized Differential

<abstract><p>In this paper, we introduce the $ q $-analogus of generalized differential operator involving $ q $-Mittag-Leffler function in open unit disk</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} E = \left \{ z:z\in \mathbb{C\ \ }\text{ and} \ \ \left \vert z\right \vert &lt;1\right \} \end{equation*} $\end{document} </tex-math></disp-formula></p> <p>and define new subclass of analytic and bi-univalent functions. By applying the Faber polynomial expansion method, we then determined general coefficient bounds $ |a_{n}| $, for $ n\geq 3 $. We also highlight some known consequences of our main results.</p></abstract>

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 Generalized Briot-Bouquet differential equation based on new differential operator with complex connections

2020 ◽  
Vol 28 (1) ◽  
pp. 105-114
Author(s):  
Rabha W. Ibrahim
Keyword(s):  
Differential Equation ◽  
Differential Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Difference Operator ◽  
Open Unit ◽  
Open Unit Disk ◽  
New Class ◽  
Generalized Operator ◽  
Generalized Differential

AbstractInequality study is a magnificent field for investigating the geometric behaviors of analytic functions in the open unit disk calling the subordination and superordination. In this work, we aim to formulate a generalized differential-difference operator. We introduce a new class of analytic functions having the generalized operator. Some subordination results are included in the sequel.

scholarly journals Further Geometric Properties of a Subclass of Univalent Functions

2020 ◽  
Vol 8 (1) ◽  
pp. 1
Author(s):  
Ezekiel A. Oyekan
Keyword(s):  
Differential Operator ◽  
Univalent Function ◽  
Univalent Functions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Geometric Properties ◽  
Generalized Differential ◽  
Necessary And Sufficient

This present paper aims to investigate further, certain characterization properties for a subclass of univalent function defined by a generalized differential operator. In particular, necessary and sufficient conditions for the function  to belong to the subclass  is established. Additionally, we provide the 𝛅-neighborhood properties for the function  by making use of the necessary and sufficient conditions. The results obtained are new geometric properties for the subclass  

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

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