scholarly journals On Sandwich Theorems for Certain Univalent Functions Defined by a New operator

2019 ◽  
Vol 11 (2) ◽  
pp. 72-80 ◽  
Author(s):  
Waggas Galib Atshan ◽  
Elaf Ibrahim Badawi
Keyword(s):  
Unit Disc ◽  
Univalent Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disc ◽  
Differential Subordination And Superordination

In this paper, we study some differential subordination and superordination results for certain univalent functions in the open unit disc U by using a new operator . Also, we derive some sandwich theorems.

scholarly journals On Differential Subordination and Superordination for Univalent Function Involving New Operator

2022 ◽  
pp. 22-31
Author(s):  
Mustafa I. Hameed ◽  
Buthyna Najad Shihab
Keyword(s):  
Integral Operator ◽  
Hadamard Product ◽  
Univalent Functions ◽  
Differential Subordination ◽  
Linear Operators ◽  
Open Unit ◽  
Open Unit Disc ◽  
Third Order ◽  
Differential Subordination And Superordination ◽  
Shed Light

The goal of this paper is to investigate some of the features of differential subordination of analytic univalent functions in an open unit disc. In addition, it has shed light on geometric features such as coefficient inequality, Hadamard product qualities, and the Komatu integral operator. Some intriguing results for third-order differential subordination and superordination of analytic univalent functions have been installed. Then, using the convolution of two linear operators, certain results of third order differential subordination involving linear operators were reported. As a result, we use features of the Komatu integral operator to analyze and study third-order subordinations and superordinations in relation to the convolution. Finally, several results for third order differential subordination in the open unit disk using generalized hypergeometric function have been addressed using the convolution operator.

scholarly journals Harmonic univalent functions defined by post quantum calculus operators

2019 ◽  
Vol 11 (1) ◽  
pp. 5-17 ◽  
Author(s):  
Om P. Ahuja ◽  
Asena Çetinkaya ◽  
V. Ravichandran
Keyword(s):  
Unit Disc ◽  
Univalent Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Open Unit Disc ◽  
Quantum Calculus ◽  
Special Cases ◽  
The Family ◽  
Covering Theorems

Abstract We study a family of harmonic univalent functions in the open unit disc defined by using post quantum calculus operators. We first obtained a coefficient characterization of these functions. Using this, coefficients estimates, distortion and covering theorems were also obtained. The extreme points of the family and a radius result were also obtained. The results obtained include several known results as special cases.

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.

Majorization-Subordination Theorems for Locally Univalent Functions, II

1973 ◽  
Vol 25 (2) ◽  
pp. 420-425 ◽  
Author(s):  
Douglas Michael Campbell
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
The Family ◽  
Linear Invariant ◽  
Linear Invariant Family

Let denote the set of all normalized analytic univalent functions in the open unit disc D. Let f(z), F(z) and φ(z) be analytic in |z| < r. We say that f(z) is majorized by F(z) in we say that f(z) is subordinate to F(z) in where .Let be the set of all locally univalent (f’(z) ≠ 0) analytic functions in D with order ≦α which are of the form f(z) = z +… . The family is known as the universal linear invariant family of order α [6]. A concise summary of and introduction to properties of linear invariant families which relate to the following material is contained in [1]. The present paper contains the proofs of some of the results announced in [1]

scholarly journals New Subclasses concerning Some Analytic and Univalent Functions

2017 ◽  
Vol 2017 ◽  
pp. 1-4
Author(s):  
Maslina Darus ◽  
Shigeyoshi Owa
Keyword(s):  
Unit Disc ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
Analytic And Univalent Functions

Considering a function f(z)=z/1-z2 which is analytic and starlike in the open unit disc U and a function f(z)=z/1-z which is analytic and convex in U, we introduce two new classes Sα⁎(β) and Kα(β) concerning fα(z)=z/1-zα  (α>0). The object of the present paper is to discuss some interesting properties for functions in the classes Sα⁎(β) and Kα(β).

scholarly journals Mapping properties of Janowski-type harmonic functions involving Mittag-Leffler function

2021 ◽  
Vol 6 (12) ◽  
pp. 13235-13246
Author(s):  
Murugusundaramoorthy Gangadharan ◽  
◽  
Vijaya Kaliyappan ◽  
Hijaz Ahmad ◽  
K. H. Mahmoud ◽  
...  
Keyword(s):  
Convolution Operator ◽  
Unit Disc ◽  
Harmonic Functions ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disc

<abstract><p>In this paper, we examine a connotation between certain subclasses of harmonic univalent functions by applying certain convolution operator regarding Mittag-Leffler function. To be more precise, we confer such influences with Janowski-type harmonic univalent functions in the open unit disc $ \mathbb{D}. $</p></abstract>

scholarly journals Coefficients assessment for certain subclasses of bi-univalent functions related with quasi-subordination

2020 ◽  
Vol 108 (122) ◽  
pp. 155-162
Author(s):  
Sibel Yalçın ◽  
Waggas Atshan ◽  
Haneen Hassan
Keyword(s):  
Univalent Function ◽  
Unit Disc ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disc

We investigate specific new subclasses of the function class ? of bi-univalent function defined in the open unit disc, which is connected with quasi-subordination. We find estimates on the Taylor-Maclaurin coefficients |a2| and |a3| for functions in these subclasses. Already pointed out are some documented and new implications of those findings.

scholarly journals Hankel determinant for certain class of analytic function defined by generalized derivative operator

2012 ◽  
Vol 43 (3) ◽  
pp. 445-453
Author(s):  
Ma'moun Harayzeh Al-Abbadi ◽  
Maslina Darus
Keyword(s):  
Analytic Function ◽  
Upper Bound ◽  
Unit Disc ◽  
Univalent Functions ◽  
Open Unit ◽  
Hankel Determinant ◽  
Open Unit Disc ◽  
Derivative Operator ◽  
Generalized Derivative ◽  
Generalised Derivatives

The authors in \cite{mam1} have recently introduced a new generalised derivatives operator $ \mu_{\lambda _1 ,\lambda _2 }^{n,m},$ which generalised many well-known operators studied earlier by many different authors. By making use of the generalised derivative operator $\mu_{\lambda_1 ,\lambda _2 }^{n,m}$, the authors derive the class of function denoted by $ \mathcal{H}_{\lambda _1 ,\lambda _2 }^{n,m}$, which contain normalised analytic univalent functions $f$ defined on the open unit disc $U=\left\{{z\,\in\mathbb{C}:\,\left| z \right|\,<\,1} \right\}$ and satisfy \begin{equation*}{\mathop{\rm Re}\nolimits} \left( {\mu _{\lambda _1 ,\lambda _2 }^{n,m} f(z)} \right)^\prime > 0,\,\,\,\,\,\,\,\,\,(z \in U).\end{equation*}This paper focuses on attaining sharp upper bound for the functional $\left| {a_2 a_4 - a_3^2 } \right|$ for functions $f(z)=z+ \sum\limits_{k = 2}^\infty {a_k \,z^k }$ belonging to the class $\mathcal{H}_{\lambda _1 ,\lambda _2 }^{n,m}$.

scholarly journals On Sandwich Theorems Results for Certain Univalent Functions Defined by Generalized Operators

2021 ◽  
pp. 2376-2383
Author(s):  
Waggas Galib Atshan ◽  
Aqeel Ahmed Redha Ali
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Differential Subordination And Superordination

In this present paper, we obtain some differential subordination and superordination results, by using generalized operators for certain subclass of analytic functions in the open unit disk. Also, we derive some sandwich results.

"Some Results of Differential Subordination and Superordination for Univalent Functions

2021 ◽  
Vol 8 (1) ◽  
pp. 91-97
Author(s):  
Ihsan A. Abbas
Keyword(s):  
Univalent Functions ◽  
Sufficient Conditions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Type Result ◽  
Best Dominant ◽  
Subordination Chain ◽  
Sandwich Type ◽  
Differential Subordination And Superordination

"Let 1 and 2 belong to a certain class of normalized analytic univalent functions in the open unit disk of the complex plane. Sufficient conditions are obtained for normalized analytic functions to satisfy the double subordination chain 1() ≺() ≺ 2() , then we obtain 1() is the best subordinant, 2() is the best dominant. Also we derive some sandwich –type result.

Sign in / Sign up

Export Citation Format

Share Document