scholarly journals Properties of a New Subclass of Analytic Functions With Negative Coefficients Defined by Using the Q-Derivative

2020 ◽  
Vol 5 (1) ◽  
pp. 303-308
Author(s):  
Roberta Bucur ◽  
Daniel Breaz
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
New Class ◽  
Coefficient Inequalities ◽  
Distortion Theorems

AbstractIn this paper we define a new class of analytic functions with negative coefficients involving the q-differential operator. Our main purpose is to determine coefficient inequalities and distortion theorems for functions belonging to this class. Connections with previous results are pointed out.

scholarly journals Difference formula defined by a new differential symmetric operator for a class of meromorphically multivalent functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Rabha W. Ibrahim ◽  
Ibtisam Aldawish
Keyword(s):  
Differential Operator ◽  
Boundary Value Problems ◽  
Unit Disk ◽  
Spectral Theory ◽  
Analytic Functions ◽  
Special Class ◽  
Symmetric Operator ◽  
New Class ◽  
Difference Formula ◽  
Symmetric Operators

AbstractSymmetric operators have benefited in different fields not only in mathematics but also in other sciences. They appeared in the studies of boundary value problems and spectral theory. In this note, we present a new symmetric differential operator associated with a special class of meromorphically multivalent functions in the punctured unit disk. This study explores some of its geometric properties. We consider a new class of analytic functions employing the suggested symmetric differential operator.

Results of differential subordination for a unified subclass of analytic functions defined using generalized Ruscheweyh derivative operator

2019 ◽  
Vol 12 (03) ◽  
pp. 1950035
Author(s):  
Ritu Agarwal ◽  
G. S. Paliwal ◽  
Parany Goswami
Keyword(s):  
Analytic Functions ◽  
Differential Subordination ◽  
Derivative Operator ◽  
Sandwich Theorem ◽  
Ruscheweyh Derivative Operator ◽  
Ruscheweyh Derivative ◽  
Principle Of Subordination ◽  
Coefficient Inequalities ◽  
Distortion Theorems

In this paper, we introduce a unified subclass of analytic functions by making use of the principle of subordination, involving generalized Ruscheweyh Derivative operator [Formula: see text]. The properties such as inclusion relationships, distortion theorems, coefficient inequalities and differential sandwich theorem for the above class have been discussed.

scholarly journals Certain Subclasses of Multivalent Functions Defined by Higher-Order Derivative

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Xiaofei Li ◽  
Deng Ding ◽  
Liping Xu ◽  
Chuan Qin ◽  
Songbo Hu
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Extreme Points ◽  
Higher Order ◽  
Order Derivative ◽  
Special Cases ◽  
Higher Order Derivative ◽  
Coefficient Inequalities ◽  
Distortion Theorems

In this paper, we define and study some subclasses of multivalent analytic functions of higher order in the unit disc. These classes generalize some classes previously studied. We obtain coefficient inequalities, distortion theorems, extreme points, and integral mean inequalities. We derive some results as special cases.

scholarly journals Generalization of certain subclasses of analytic functions

1987 ◽  
Vol 10 (4) ◽  
pp. 725-732 ◽  
Author(s):  
Tadayuki Sekine
Keyword(s):  
Fractional Calculus ◽  
Analytic Functions ◽  
Coefficient Inequalities ◽  
Distortion Theorems

We introduce the subclassTj(n,m,α)of analytic functions with negative coefficients by the operatorDn. Coefficient inequalities and distortion theorems of functions inTj(n,m,α)are determind. Further, distortion theorems for fractional calculus of functions inTj(n,m,α)are obtained.

scholarly journals Coefficient Estimates and Other Properties for a Class of Spirallike Functions Associated with a Differential Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Halit Orhan ◽  
Dorina Răducanu ◽  
Murat Çağlar ◽  
Mustafa Bayram
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Upper Bounds ◽  
Coefficient Estimates ◽  
New Class ◽  
Spirallike Functions

For , , , , and , a new class of analytic functions defined by means of the differential operator is introduced. Our main object is to provide sharp upper bounds for Fekete-Szegö problem in . We also find sufficient conditions for a function to be in this class. Some interesting consequences of our results are pointed out.

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 A certain subclass of multivalent functions involving higher-order derivatives

Filomat ◽  
2016 ◽  
Vol 30 (1) ◽  
pp. 113-124 ◽  
Author(s):  
H.M. Srivastava ◽  
Rabha El-Ashwah ◽  
Nicoleta Breaz
Keyword(s):  
Integral Operator ◽  
Hadamard Product ◽  
Extreme Points ◽  
Function Class ◽  
Higher Order ◽  
New Class ◽  
Coefficient Inequalities ◽  
Distortion Theorems

In this paper we introduce and study a new class of analytic and p-valent functions involving higher-order derivatives. For this p-valent function class, we derive several interesting properties including (for example) coefficient inequalities, distortion theorems, extreme points, and the radii of closeto-convexity, starlikeness and convexity. Several applications involving an integral operator are also considered. Finally, we obtain some results for the modified Hadamard product of the functions belonging to the p-valent function class which is introduced here.

DIFFERENTIAL SUBORDINATION RESULTS FOR ANALYTIC FUNCTIONS

2013 ◽  
Vol 06 (04) ◽  
pp. 1350044
Author(s):  
Rabha M. El-Ashwash ◽  
Mohamed K. Aouf ◽  
Maslina Darus
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Differential Subordination ◽  
New Class ◽  
Inclusion Properties

In this paper, a new class of analytic functions is introduced on the unit disk U which is defined by a certain differential operator. Some inclusion properties are discussed. Indeed, three other classes are also introduced and some differential subordination results 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 On a class of analytic functions associated to a complex domain concerning q-differential-difference operator

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Rabha W. Ibrahim ◽  
Maslina Darus
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Existence Of Solutions ◽  
Difference Operator ◽  
Open Unit ◽  
Convolution Product ◽  
Open Unit Disk ◽  
Current Investigation ◽  
Quantum Calculus ◽  
New Class

AbstractIn our current investigation, we apply the idea of quantum calculus and the convolution product to amend a generalized Salagean q-differential operator. By considering the new operator and the typical version of the Janowski function, we designate definite new classes of analytic functions in the open unit disk. Significant properties of these modules are considered, and recurrent sharp consequences and geometric illustrations are realized. Applications are considered to find the existence of solutions of a new class of q-Briot–Bouquet differential equations.

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