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 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.

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 Fractional differential superordination

2014 ◽  
Vol 45 (3) ◽  
pp. 275-284
Author(s):  
Rabha W. Ibrahim
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Fractional Order ◽  
Analytic Functions ◽  
Dual Problem ◽  
Differential Subordination ◽  
Geometric Properties ◽  
Differential Superordination ◽  
Fractional Differential ◽  
Admissible Functions

The notion of differential superordination was introduced by S.S. Miller and P.T. Mocanu as a dual concept of differential subordination. Recently, in Tamkang J. Math.[7], the author have introduced the notion of fractional differential subordination. In this work, we consider the dual problem of determining properties of analytic functions that satisfy the fractional differential superordination. By employing some types of admissible functions, involving differential operator of fractional order, we illustrate geometric properties such as starlikeness and convexity for a class of analytic functions in the unit disk. Moreover, applications are posed in the sequel.

scholarly journals Differential Sandwich Theorems for a Certain Class of Analytic Functions Defined by Differential Operator

2019 ◽  
pp. 209-220
Author(s):  
Abbas Kareem Wanas ◽  
Hala Abbas Mehai
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Hadamard Product ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
First Order ◽  
Differential Subordination And Superordination

In this paper, we establish some applications of first order differential subordination and superordination results involving Hadamard product for a certain class of analytic functions with differential operator defined in the open unit disk. These results are applied to obtain sandwich results.

scholarly journals The concept of fractional differential subordination

2013 ◽  
Vol 44 (1) ◽  
pp. 53-60
Author(s):  
Rabha W. Ibrahim
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Fractional Order ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Fractional Operators ◽  
Geometric Properties ◽  
Fractional Differential ◽  
Admissible Functions

In this work, we consider a definition for the concept of fractional differential subordination in sense of Srivastava-Owa fractional operators. By employing some types of admissible functions, involving differential operator of fractional order, we illustrate geometric properties such as starlikeness and convexity for a class of analytic functions in the unit disk. Moreover, applications are posed in the sequel.

scholarly journals Some Subordination Results for Fractional Integral Involving Wanas Differential Operator

2020 ◽  
pp. 199-205
Author(s):  
Abbas Kareem Wanas
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Fractional Integral ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk

In the present paper, we establish some differential subordination properties for analytic functions defined in the open unit disk associated with the fractional integral by using Wanas differential operator.

scholarly journals Strong Differential Subordination Results for Multivalent Analytic Functions Associated with Dziok-Srivastava Operator

2019 ◽  
pp. 159-168
Author(s):  
Abbas Kareem Wanas ◽  
Hala Abbas Mehdi
Keyword(s):  
Unit Disk ◽  
Complex Plane ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Closed Unit Disk ◽  
Strong Differential Subordination

In this paper, by making use of the principle of strong subordination, we establish some interesting properties of multivalent analytic functions defined in the open unit disk and closed unit disk of the complex plane associated with Dziok-Srivastava operator.

scholarly journals Some Applications of Second-Order Differential Subordination on a Class of Analytic Functions Defined by Komatu Integral Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Serap Bulut
Keyword(s):  
Integral Operator ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Second Order ◽  
New Class

We introduce a new class of analytic functions by using Komatu integral operator and obtain some subordination results.

scholarly journals Differential Subordination Results for Analytic Functions in the Upper Half-Plane

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Huo Tang ◽  
M. K. Aouf ◽  
Guan-Tie Deng ◽  
Shu-Hai Li
Keyword(s):  
Unit Disk ◽  
Half Plane ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Upper Half Plane ◽  
Admissible Functions

There are many articles in the literature dealing with differential subordination problems for analytic functions in the unit disk, and only a few articles deal with the above problems in the upper half-plane. In this paper, we aim to derive several differential subordination results for analytic functions in the upper half-plane by investigating certain suitable classes of admissible functions. Some useful consequences of our main results are also pointed out.

scholarly journals SOME INCLUSION PROPERTIES FOR CERTAIN K-UNIFORMLY SUBCLASSES OF ANALYTIC FUNCTIONS ASSOCIATED WITH WRIGHT FUNCTION

2019 ◽  
Vol 7 (9) ◽  
pp. 218-229
Author(s):  
E. E. Ali
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Integral Operators ◽  
Special Property ◽  
Open Unit ◽  
Open Unit Disk ◽  
Wright Function ◽  
Inclusion Properties

A new operator  is introduced for functions of the form   which are analytic in the open unit disk . We introduce several inclusion properties of the new k-uniformly classes , ,    and    of analytic functions defined by using the Wright function with the operator    and the main object of this paper is to investigate various inclusion relationships for these classes. In addition, we proved that a special property is preserved by some integral operators.

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