Some Properties of the Class of Univalent Functions Involving a New Generalized Differential Operator

2016 ◽  
Vol 13 (10) ◽  
pp. 6797-6799
Author(s):  
A. A Amourah ◽  
T Al-Hawary ◽  
M Darus
Keyword(s):  
Differential Operator ◽  
Integral Operator ◽  
Univalent Functions ◽  
Open Unit ◽  
Coefficient Estimates ◽  
Open Unit Disc ◽  
Closure Theorems ◽  
Distortion Theorems ◽  
Generalized Differential ◽  
Growth And Distortion Theorems

The main purpose of this paper is to introduce new generalized differential operator Aμm, λ(α,β)f(z) defined in the open unit disc U = {z ∈ : |z| < 1}. We then, using this operator to introduce novel subclass Ωm*(δ,λ,α,β,b) by using the operator Aμm, λ(α,β)f(z). Then, we discuss coefficient estimates growth and distortion theorems, closure theorems and integral operator.

scholarly journals Some properties of a class of analytic functions involving a new generalized differential operator

2019 ◽  
Vol 38 (6) ◽  
pp. 33-42 ◽  
Author(s):  
A. A. Amourah ◽  
Feras Yousef
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Coefficient Estimates ◽  
Alpha Beta ◽  
Distortion Theorems ◽  
Generalized Differential ◽  
Growth And Distortion Theorems

In the present paper, we introduce a new generalized differentialoperator $A_{\mu,\lambda,\sigma}^{m}(\alpha,\beta)$ defined on the openunit disc $U=\left\{ z\in%%TCIMACRO{\U{2102} }%%BeginExpansion\mathbb{C}:\left\vert z\right\vert <1\right\} $. A novel subclass $\Omega_{m}^{\ast}(\delta,\lambda,\alpha,\beta,b)$ by means of the operator $A_{\mu,\lambda,\sigma}^{m}(\alpha,\beta)$ is also introduced. Coefficient estimates, growth and distortion theorems, closuretheorems, and class preserving integral operators for functions in the class $\Omega_{m}^{\ast}(\delta,\lambda,\alpha,\beta,b)$ are discussed. Furthermore, sufficient conditions for close-to-convexity, starlikeness, and convexity for functions in the class $\Om are obtained

scholarly journals On Subclass of Analytic Univalent Functions Associated with Negative Coefficients

2010 ◽  
Vol 2010 ◽  
pp. 1-11
Author(s):  
Ma'moun Harayzeh Al-Abbadi ◽  
Maslina Darus
Keyword(s):  
Analytic Functions ◽  
Univalent Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Derivative Operator ◽  
Generalized Derivative ◽  
Closure Theorems ◽  
Coefficient Inequalities ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems

M. H. Al-Abbadi and M. Darus (2009) recently introduced a new generalized derivative operatorμλ1,λ2n,m, which generalized many well-known operators studied earlier by many different authors. In this present paper, we shall investigate a new subclass of analytic functions in the open unit diskU={z∈ℂ:|z|<1}which is defined by new generalized derivative operator. Some results on coefficient inequalities, growth and distortion theorems, closure theorems, and extreme points of analytic functions belonging to the subclass are obtained.

scholarly journals Properties of Certain Subclass of Meromorphic Multivalent Functions Associated with q-Difference Operator

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1035
Author(s):  
Cai-Mei Yan ◽  
Rekha Srivastava ◽  
Jin-Lin Liu
Keyword(s):  
Difference Operator ◽  
Necessary Conditions ◽  
Partial Sums ◽  
Coefficient Estimates ◽  
Radius Of Starlikeness ◽  
Closure Theorems ◽  
Sufficient And Necessary Conditions ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems

A new subclass Σp,q(α,A,B) of meromorphic multivalent functions is defined by means of a q-difference operator. Some properties of the functions in this new subclass, such as sufficient and necessary conditions, coefficient estimates, growth and distortion theorems, radius of starlikeness and convexity, partial sums and closure theorems, are investigated.

scholarly journals A Class of p-valent Functions in the Punctured Disc

2019 ◽  
pp. 473-481
Author(s):  
Olubunmi A. Fadipe-Joseph ◽  
K. O. Dada
Keyword(s):  
Differential Operator ◽  
Coefficient Estimates ◽  
Alpha Beta ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems

Motivated by Aouf differential operator, a class $F_{\lambda, p}^{n}\left ( \alpha , \beta , \gamma \right )$ of p-valent functions in the punctured disc $U^{*}=\left \{ z:0<\left | z \right |<1 \right \}=U\setminus \left \{ 0 \right \} $ is defined. The coefficient estimates, growth and distortion theorems for the class are obtained.

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 Some new Results of a Subclass of Meromorphic Univalent Functions with Negative Coefficients Defined by liu – Srivastava Linear Operator

2018 ◽  
Vol 7 (4.36) ◽  
pp. 806
Author(s):  
Amal Mohammed Darweesh
Keyword(s):  
Linear Operator ◽  
Univalent Functions ◽  
Partial Sums ◽  
Closure Theorems ◽  
Distortion Theorems ◽  
Convolution Properties ◽  
Growth And Distortion Theorems ◽  
Meromorphic Univalent Functions

In this paper, we introduce and study a new subclass of meromorphic univalent functions with negative coefficients defined by Liu – Srivastava linear operator in the  We obtain some properties like, coefficients inequalities, growth and distortion theorems, closure theorems, partial sums and convolution properties.  

scholarly journals Subclasses of Bi-Univalent Functions Defined by Frasin Differential Operator

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 783 ◽  
Author(s):  
Ibtisam Aldawish ◽  
Tariq Al-Hawary ◽  
B. A. Frasin
Keyword(s):  
Analytic Function ◽  
Differential Operator ◽  
Unit Disc ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Open Unit Disc ◽  
Class A ◽  
Class Of Functions

Let Ω denote the class of functions f ( z ) = z + a 2 z 2 + a 3 z 3 + ⋯ belonging to the normalized analytic function class A in the open unit disk U = z : z < 1 , which are bi-univalent in U , that is, both the function f and its inverse f − 1 are univalent in U . In this paper, we introduce and investigate two new subclasses of the function class Ω of bi-univalent functions defined in the open unit disc U , which are associated with a new differential operator of analytic functions involving binomial series. Furthermore, we find estimates on the Taylor–Maclaurin coefficients | a 2 | and | a 3 | for functions in these new subclasses. Several (known or new) consequences of the results are also pointed out.

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 Some subclasses of analytic functions of complex order defined by new differential operator

2012 ◽  
Vol 43 (2) ◽  
pp. 223-242
Author(s):  
Maslina Darus ◽  
Imran Faisal
Keyword(s):  
Differential Operator ◽  
Extreme Points ◽  
Coefficient Estimates ◽  
Integral Means ◽  
Fractional Differential Operator ◽  
Alpha Omega ◽  
Fractional Differential ◽  
Alpha Beta ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems

Let \hskip 2pt $\mathcal{A}(n)$ \hskip 2pt denote \hskip 2pt the \hskip 2pt class \hskip 2pt of \hskip 2pt analytic \hskip 2pt functions \hskip 2pt $f$ \hskip 2pt in \hskip 2pt the \hskip 2pt open \hskip 2pt unit \hskip 2pt disk \hskip 2pt $U=\{z:|z|<1\}$ \hskip 2pt normalized \hskip 2pt by \hskip 2pt $f(0)=f'(0)-1=0.$ \hskip 2pt In \hskip 2pt this \hskip 2pt paper, \hskip 2pt we \hskip 2pt introduce \hskip 2pt and \hskip 2pt study \hskip 2pt the \hskip 2pt classes \hskip 2pt $S_{n, \mu}(\gamma, \alpha, \beta, \lambda, \mho)$ \hskip 2pt and \hskip 2pt $R_{n, \mu}(\gamma, \alpha, \beta, \lambda, \mho)$ \hskip 2pt of \hskip 2pt functions \hskip 2pt $f\in\mathcal{A}(n)$ with $(\mu)z(D^{\mho+2}_{\lambda}(\alpha, \omega)f(z))'+(1-\mu)z(D^{\mho+1}_{\lambda}(\alpha, \omega)f(z))'\neq0$ and satisfy some conditions available in literature, where $f\in\mathcal{A}(n), \alpha, \omega, \lambda, \mu \geq0, \mho\in \mathbb{N}\cup\{0\},\,\,z\in U,$ and $D^{m}_{\lambda}(\alpha, \omega)f(z): \mathcal{A}\rightarrow \mathcal{A},$ is the linear fractional differential operator, newly defined as follows $$D^{m}_{\lambda}(\alpha, \omega)f(z) = z+ \sum\limits_{k=2}^{\infty}a_{k}(1+(k-1)\lambda \omega^{\alpha})^{m}z^{k}\cdot$$ Several properties such as coefficient estimates, growth and distortion theorems, extreme points, integral means inequalities and inclusion for the functions included in the classes $S_{n, \mu}(\gamma, \alpha, \beta, \lambda, \mho, \omega)$ and $R_{n, \mu}(\gamma, \alpha, \beta, \lambda, \mho, \omega)$ are given.

scholarly journals Maclaurin Coefficient Estimates of Bi-Univalent Functions Connected with the q-Derivative

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 418 ◽  
Author(s):  
Sheza M. El-Deeb ◽  
Teodor Bulboacă ◽  
Bassant M. El-Matary
Keyword(s):  
Unit Disc ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Coefficient Estimates ◽  
Open Unit Disc

In this paper we introduce a new subclass of the bi-univalent functions defined in the open unit disc and connected with a q-analogue derivative. We find estimates for the first two Taylor-Maclaurin coefficients a 2 and a 3 for functions in this subclass, and we obtain an estimation for the Fekete-Szegő problem for this function class.

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